This article has been accepted for publication in The British Journal for the Philosophy ofScience. This is a preprint draft produced by the author. Please do not cite this version.

Many Meanings of “Heuristic”

Sheldon J. Chowsheldonjchow@gmail.comDepartment of PhilosophyMount Allison University

Abstract A survey of contemporary philosophical and scientific literatures reveals thatdifferent authors employ the term “heuristic” in ways that deviate from, and are sometimesinconsistent with, one another. Given its widespread use in philosophy and cognitive sciencegenerally, it is striking that there appears little concern for a clear account of what phenomenaheuristics pick out or refer to. In response, I consider several accounts of “heuristic”, andI draw a number of distinctions between different sorts of heuristics in order to make senseof various research programmes. I then develop a working characterization of “heuristic”which is shown to be coherent and robust enough to serve as a kind within philosophy andcognitive science broadly. My intent is not to pursue a unified account of “heuristic”, but tohighlight some features of certain kinds of heuristics that are important for theorizing aboutcognition in order to proceed with a science of the mind/brain.

The term ‘heuristic’ and its cognates are widely used to label certain methods or

procedures that guide inference and/or judgement in problem-solving and decision-making.

Heuristics are commonly understood as economical shortcut procedures that may not lead

to optimal or correct results, but will generally produce outcomes that are in some sense

satisfactory or ‘good enough’. It is also widely acknowledged that heuristics can result in

systematic errors or mistakes. But all this is usually understood as a trade-off: heuristics

forego optimal outcomes in favour of economy; systematic errors may result on some

occasions, but they tend to produce sufficient solutions. And indeed, some sort of

evolutionary/adaptation story is often told to explain our use of and reliance on heuristics

in our day-to-day reasoning. Understood as such, it is received wisdom that heuristics are a

stock commodity in human cognition.

However, while it is agreed that humans use and generally rely on heuristics, a close

inspection of the philosophical and scientific literatures reveals that different authors

employ the term ‘heuristic’ in ways that deviate from one another, and are sometimes

inconsistent with one another. Not only is ‘heuristic’ used in diverse ways across and

within disciplines, but its meaning has evolved over the years. Consequently, as Jonathan

St.B.T. Evans ([2009], p. 36) remarks, ‘The term “heuristic” is deeply ambiguous’. Indeed,

the term very well may not express a single, unified concept. Or perhaps ‘heuristic’ is best

characterised in terms of a cluster of family resemblances. In any case, given its widespread

use in philosophy and cognitive science generally, it is striking to see that, while there isn’t

a consensus on what phenomena ‘heuristics’ pick out or refer to, little philosophical

attention has been paid to providing an appropriate characterisation, or characterisations,

of ‘heuristic’. We’re long overdue for such a task. It is unacceptable that philosophers

continue to offer accounts of reasoning, for example, while invoking an ambiguous term (see

Bechtel and Richardson [2010]; Hooker [2011]; Wimsatt [2007]); moreover, cognitive science

needs to be clear on its objects of study.

All this prompts the twofold aim of this paper, which is to clarify (some of) the many

uses of ‘heuristic’, and to offer an adequate working characterisation of the term to apply

to a specified range of cognitive phenomena. I should like to be clear that my intent is not

to pursue a unified account of ‘heuristic’, but to highlight some features of heuristics that

are important for theorising about reasoning and cognition, and to develop an account of

‘heuristic’ which is useful for proceeding with a science of the mind/brain. I begin, in

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section 1, by fleshing-out the motivation for demanding an appropriate characterisation, or

characterisations, of ‘heuristic’. In section 2, I discuss some definitions of the term, and I

give an extensive treatment of a generalised negative definition that is often found in the

literature. In section 3, I draw on the work of some influential heuristics researchers,

including George Polya, Herbert Simon, Daniel Kahneman and Amos Tversky, and Gerd

Gigerenzer. By considering the various accounts of these thinkers, we will be in a position

to make a number of distinctions between different kinds of heuristics. The result is an

initial taxonomy of heuristics which will help us to make sense of various claims made

about human cognition and of various research programmes. This taxonomy also enables

me to focus on a specific class of heuristics; in section 4 I develop a working characterisation

of these sorts of heuristics. I close in section 5 with some concluding remarks.

1 Why We Need an Appropriate Characterisation of ‘Heuristic’

Given its widespread use within (and without) the several disciplines of cognitive science, it

is intriguing that there is little concern for a fully developed characterisation of ‘heuristic’.

The lack of a developed characterisation of the term is disconcerting in at least two ways.

First, since heuristics have rapidly made their way as central tenets in many theories of

reason and cognition, we might expect something that approaches a refined and robust

explication of what is meant by ‘heuristic’. But, as far as I know, no one has produced such

an explication. This is problematic for cognitive science since, if it is indeed a science,

careful consideration should be taken to delimit heuristics qua entities of scientific theories.

To put it another way, if cognitive science is in the business of discovering and studying the

kinds within its domain, pains should be taken to appropriately characterise these kinds

(Carruthers [2006]; Pylyshyn [1999]); by all accounts, heuristics are included among the

kinds of cognitive science. Thus, being clear on what phenomena are picked out by

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‘heuristic’ should be of concern to both scientists and philosophers who wish to make sense

of, and perhaps adopt, any theory of reason or cognition that claims a role for heuristics.

Secondly, many arguments—descriptive and normative—are made on the premise that

heuristics are ubiquitous in human cognition. Such arguments try to decide the extent to

which humans rely on heuristics, what heuristics people employ in what circumstances, or

whether and when it is rational to engage heuristics. But vagueness (or perhaps ambiguity)

in the concepts employed by a theory will be inherited by any arguments based on that

theory. Unclarity in what heuristics are in the first place therefore impedes progress on

matters involving the purported uses and abuses of heuristics in reasoning (taken here to

include judgement, inference, problem-solving, and decision-making).1 In the face of

vagueness (or ambiguity) in concepts, the arguments concerning human reasoning may very

well lack a sufficient basis to be anywhere near decisive. To be sure, if we do not know

what cognitive processes ‘heuristics’ refer to, then it is unclear whether and to what extent

purported heuristics have a role in our cognitive lives. For instance, there has been a

longstanding debate between those who believe that heuristic strategies are or can be

rational, and those who believe that rationality resides in the dictates of some

independently established normative theory which heuristics fail to meet (see Simon [1957];

Gigerenzer [1996]; Kahneman and Tversky [1996]; Samuels, Stich and Bishop [2002]). But

if it is unclear what either party means by ‘heuristic’, then the force of the arguments from

either side of the debate, or precisely what is being claimed, is equally unclear. This is

illustrated by Gigerenzer’s ([1996]) accusation that Kahneman and Tversky deploy vague

labels instead of describing real heuristics (see also Gigerenzer and Todd [1999]; Gigerenzer

and Brighton [2009]), and Kahneman and Tversky’s ([1996], p. 585) response that the

1My uses throughout this paper of terms such as ‘reason’, ‘inference’, ‘decision-making’ and the likeshould be understood in very broad senses.

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heuristics they study may nevertheless be ‘assessed empirically; hence need not be defined

a priori’. We might thus see that, since a proper characterisation of ‘heuristic’ is

lacking—or at least a characterisation on which each camp can agree is lacking—the debate

concerning whether and which heuristics are (or can be) rational can scarcely advance, and

the deeper issue about the nature of rationality gets lost in confusion.

In sum, I perceive at least two significant problems arising from the absence of a clear

and robust characterisation of ‘heuristic’. The first problem concerns heuristics as objects

of scientific study; the second problem concerns arguments that invoke heuristics to make

descriptive and/or normative claims about human cognition. These two problems (perhaps

among others) act as barriers that inhibit the advancement of philosophical and scientific

research on reasoning and cognition. To overcome these barriers, we need an account of

heuristics that, on the one hand, is coherent and robust enough to plausibly fit a scientific

kind,2 and on the other hand, provides clarity in the objects of study. To the extent that

an account of heuristics is successful with respect to these tasks, we will better understand

how the mind/brain works and how heuristics fit within the various conceptual frameworks

of psychology and the rest of the cognitive sciences.

Before continuing on, it is important to forestall a worry that may be raised against the

project of this paper. One may claim that an attempt at characterising ‘heuristic’ may be

neither possible nor useful if the class of heuristics is constituted by phenomena that share

a family resemblance.3 If ‘heuristic’ is a term used by scientists or philosophers to refer to

2I prefer to use ‘scientific kind’ as opposed to ‘natural kind’, since I’m not prepared to argue that heuristicsare natural kinds. I take a scientific kind to be something that is a proper object of scientific study. Inthis sense, whatever else a scientific kind may be, it had better be suitably characterised to play a certain(perhaps explanatory) role in a scientific theory. Suitability and level of characterisation will come in degrees,I suppose, depending on the role that the kind is supposed to play in the theory in question. Whatever thecase may be, it is beyond the scope of this paper to develop or defend a theory of scientific kinds. The point Iam making in the main text is that ‘heuristic’ generally isn’t adequately characterised to be a proper objectof scientific study, or for it to play the role many researchers assume it to play in scientific theories.

3I thank an anonymous referee for raising this concern.

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certain cognitive or perceptual processes whose properties overlap in various ways with one

another, then it would be futile to attempt to identify the core properties of heuristics.

Moreover, what processes are referred to as ‘heuristic’ may very well depend on the aims of

the theory and research in question, and this seems to vitiate the need for a definite

characterisation of the term.

Though this is a natural worry to have, it is not one that bears negatively on the

project of this paper. In the first instance, given the lack of work on characterising

‘heuristic’, it has yet to be determined whether the term is best characterised as a cluster

of family resemblances; so far as we presently know, this may not be the case. So some

value in this project can be found in initiating interest and research to make such a

determination, as well as in going some way to providing such a determination. Yet, even if

‘heuristic’ does consist of a cluster of family resemblances, again given the lack of work on

characterising the term, it is worthwhile to identify the relevant properties that make up

the family resemblances, for this would allow us to better understand various perceptual

and cognitive processes as heuristic. As we shall see, a close examination of several

phenomena that researchers call ‘heuristic’ reveals a number of relevant properties, which

allows for a classification of the phenomena into distinguishable kinds (section 3).

If we take our cue from Edouard Machery’s ([2009]) treatment of ‘concept’ or Marc

Ereshefsky’s ([1998], [2001]) treatment of ‘species’, we might suspect that a treatment of

‘heuristic’ will likewise result in a pluralistic conception of the term.4 And indeed, the

treatment I give below seems to suggest a sort of pluralism as it considers the many uses of

‘heuristic’ in the literature. In this light, the present project has two chief importances.

4Yet whereas Machery’s and Ereshefsky’s work each followed from a history of thinkers who have at-tempted to advance precise accounts of these respective concepts, the situation for ‘heuristic’ is differentsince there is generally a lack of any attempt at a detailed account of the term. Since the work must beginsomewhere, it is my hope that this paper serves as a fruitful start to more thorough treatments of ‘heuristic’,even if it turns out to be pluralistic.

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First, by trimming, pruning, and clearing away some of the brush that is the current state

of the uses of ‘heuristic’ in science and philosophy, we are put in a better position to

understand current and past research and/or arguments involving heuristics (in psychology,

computer intelligence, philosophy of science, and so on). More specifically, we will be able

to better understand what sorts of processes or phenomena are being researched or referred

to, and this will help us to navigate and make sense of much of the relevant work to date.

Second, the clarification provided in this paper can serve as a guide for future research.

Being clear, on the one hand, on the sorts of phenomena we call ‘heuristic’, and on the

other hand, on why we call such phenomena ‘heuristic’, allows us to structure various

problems for the scientist and philosopher, and it provides the materials to build

frameworks to conduct research and/or advance arguments. When, in section 4, I go on to

develop a working characterisation of ‘heuristic’, I identify a cluster of properties possessed

by heuristics of a certain sort. This advances the clarification project with respect to a

specific class of heuristics, providing an understanding of the respects in which heuristics in

this class relate to one another (what makes them fall within a class) and the ways in

which they relate to heuristics and other processes falling outside the class. All this

contributes to identifying the heuristics of interest as scientific kinds, thus remedying the

problems discussed above. At the same time, the working characterisation I develop is

open to revision, so we leave open the possibility of recharacterisations in light of further

evidence and analysis, which is exactly what we should expect of proper scientific kinds.

2 Inadequate Definitions

2.1 A positive attempt

Psychologist Gerd Gigerenzer is arguably the most prominent researcher of heuristics

today. Since the 1990s, Gigerenzer and his colleagues have investigated how heuristics can

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produce reasonable or appropriate solutions in different ecological contexts. (For collections

of this work, see Gigerenzer et al. [1999]; Gigerenzer et al. [2011]; Todd et al. [2012].).) In

a recent review article written with Wolfgang Gaissmaier, the following definition is

proposed.

HG A heuristic is a strategy that ignores part of the information, with the goal

of making decisions more quickly, frugally, and/or accurately than more

complex methods. (Gigerenzer and Gaissmaier [2011], p. 454; see also

Todd et al. [2012], p. 7)

It is unfortunate, however, that Gigerenzer and Gaissmaier only devote a short paragraph

to discussing this definition.5 For given the motivations for the present paper, a more

extensive treatment would be appreciated, if not expected. And indeed, HG is inadequate

as a general characterisation of heuristics.

A serious problem for HG concerns the unspecified ‘more complex methods’ that

heuristics are supposed to perform more quickly, frugally and/or accurately than. For there

will always be arbitrarily more complex methods with which to make decisions. If taken as

stated, HG allows that linear regression is a heuristic insofar as part of the information is

ignored (example: under the weak exogeneity assumption, errors in predictor values are

ignored), and decisions are made more quickly, frugally, and/or accurately than other more

complex methods (example: linear regression plus Bayesian analysis, or relaxed linear

regression which drops the weak exogeneity assumption). The arbitrariness of complexity

resides in always being able to add to a decision method. Of course, Gigerenzer would not

enjoy this result; indeed, linear regression is a procedure with which he contrasts (at least

5Though see (Gigerenzer and Todd [1999]) for a lengthier discussion. Gigerenzer and Todd define ‘fast andfrugal heuristics’ thus: ‘Fast and frugal heuristics employ a minimum of time, knowledge, and computationto make adaptive choices in real environments’ (p. 14). This earlier definition is in some ways better thanGigerenzer’s more recent attempt.

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some) heuristics (see Gigerenzer and Brighton [2009]). More generally, it obvious from

Gigerenzer’s body of work that formal, complex, information-hungry procedures (such as

linear regression or Pareto/negative binomial distribution models) would not be

understood as heuristic by any means.6

Perhaps the most problematic worry for HG is that its central claim that heuristics

ignore ‘part of the information’ puts tight constraints on the types of strategies we would

consider heuristic. This can be seen once we question what ‘the’ information is supposed to

be. It is suggested by the discussion in (Gigerenzer and Gaissmaier [2011]), and it is made

explicit in (Gigerenzer and Brighton [2009], p. 111), that ignoring ‘part of the information’

means ‘ignoring cues, weights, and dependencies between cues’. But this is inadequate for

a general characterisation of heuristics, since there are strategies and procedures that seem

obviously heuristic but do not in any obvious sense ignore cues, weights, or dependencies

between cues; for example: ‘If you can’t solve a problem right away, try an indirect proof’.

What is more, some obviously heuristic strategies don’t seem to ignore information

simpliciter in any obvious way; for example: ‘Draw a diagram when trying to solve a

problem’ (in fact, this heuristic appears to require the use and integration, rather than the

ignoring, of more information, i.e., using and integrating visual information with semantic

information). (These examples of heuristics are from Polya [1957]; we shall see them again

below.) Hence, the central claim that heuristics ignore ‘part of the information’ puts too

narrow constraints on the sorts of strategies or procedures we would call ‘heuristic’—so

narrow that some strategies that are rightly considered heuristic are excluded. This is an

6Of course, the details of Gigerenzer’s work implicitly indicates the ‘more complex methods’ againstwhich heuristics perform more quickly, frugally and/or accurately, as he often compares the performance ofheuristics to the performance of regression models and Pareto/negative binomial distribution models (seeGigerenzer and Brighton [2009]). However, though Gigerenzer uses these latter models as paradigmaticof ‘more complex methods’, my argument is that, since arbitrarily more complex methods can always bederived, these paradigmatic ‘more complex methods’ can easily be characterised as heuristic according toHG.

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undesirable result.

In light of these criticisms, it is clear that HG fails to provide us with a suitable or

robust characterisation of ‘heuristic’.7 We must do better.

Yet many researchers do not even bother to provide even a simple definition, taking its

meaning to be intuitive or obvious, when in fact it is not. As Simon and his colleagues once

remarked, ‘[“heuristic”] denotes an intuitive notion usually misunderstood when

oversimplified’ (Simon et al. [1967], p. 10). At the same time, some authors provide merely

perfunctory definitions, without any concern for whether the implicated concept is coherent

or robust in the above sense.8 I shall consider such perfunctory definitions next.

2.2 Heuristics vs. guaranteed correct outcomes

A common feature of almost all perfunctory accounts of heuristics is that ‘heuristic’ is

negatively defined (cf. Fodor [2008], p. 116). A heuristic is thus understood to be deficient

or inadequate in some respect. Indeed, one often happens upon a definition which states

that heuristics are procedures that can produce good outcomes but don’t guarantee correct

solutions (see Dunbar [1998]) or don’t always work (Fodor [2008]). In one textbook on

cognition, it is claimed that a ‘hallmark’ of a heuristic approach to solving a problem is

that ‘It will work part of the time or for part of the answer, but it is very unlikely to

furnish the complete, accurate answer’ (Ashcraft [2002], p. 465). At other times one finds

7As we shall see, the working characterisation of heuristic I develop below will have some features incommon with HG. To my knowledge Gigerenzer, with his HG definition, has come the closest to providingan adequate characterisation of heuristics, my criticisms notwithstanding. Nevertheless, it will becomeapparent as we move along that the characterisation I develop is broader, encompassing a wider variety ofcognitive phenomena. Additionally, I draw several distinctions (absent in Gigerenzer’s account) to delineatedifferent kinds of heuristics (for example, differences that distinguish Gigerenzer-style heuristics from Polya-style heuristics).

8For example, in an influential book entitled Heuristics, Judea Pearl ([1984]) expounds and discussesseveral heuristics used in computation and computer science. Throughout the entire book, however, thereare only two brief passages in which he attempts to characterise heuristics (see pp. vii; 3). Though I won’tpursue the issue here, I submit that these brief passages fail to do justice to a clear understanding of whatheuristics are.

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heuristics contrasted with algorithms (see Haugeland [1981]; Richardson [1998]), where

algorithms are understood as procedures that, when applied properly, invariably produce

correct outcomes; hence, heuristics are conceived simply as procedures that do not

invariably produce correct outcomes.

Jerry Fodor’s remarks in The Language of Thought wonderfully illustrate the

distinction between procedures that are supposed to guarantee right answers and shortcut

procedures that avoid excessive mechanical computations (i.e., heuristics):

In short, the computational load associated with the solution of a class of

problems can sometimes be reduced by opting for problem-solving procedures

that work only most of the time. Reliability is wagered for efficiency in such

cases, but there are usually ways of hedging the bet. Typically, heuristic

procedures are tried first; relatively slower, but relatively algorithmic,

procedures are ‘called’ when the heuristics fail. The way of marshaling the

available computational resources can often provide the optimal trade-off

between the speed of computation and the probability of getting the right

results. (Fodor [1975], pp. 166–7)

This sort of characterisation of heuristics is not surprising in light of the fact that there is

typically a risk of suffering negative consequences for cutting corners or taking shortcuts.

As Fodor ([1975], p. 166) remarks, ‘one can often get away with less than strict compliance

with such requirements [that guarantee a correct solution] so long as one is willing to

tolerate occasional mistakes’. Yet, certainly it is not the intended purpose of heuristics to

make mistakes. Rather they offer a computationally economical method of solving a

problem. Thus understood, heuristics offer a way to cut down on the computations needed

to arrive at a desired outcome.

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Acknowledging the benefits afforded by heuristic procedures is very important in

understanding the nature of heuristics. For we would hesitate to call a procedure that

invariably leads to disaster a heuristic procedure; nor would we want to call a procedure

that is irrelevant to the task at hand a heuristic procedure (with respect to the task). Yet

such procedures most certainly would not guarantee correct outcomes. Therefore, what

heuristics fail to achieve (viz. reliably getting the right results) should be thought of as a

corollary of a definition of ‘heuristic’, rather than made to be an essential feature.

Nevertheless, notice from Fodor’s remarks that the benefits offered by heuristics are

contrasted with associated risks of making mistakes—whatever good heuristics do, they do

not always get things right. In this way, Fodor provides a particularly clear example of the

attitude toward heuristics that typically leads to a negative characterisation in terms of

what they fail to do, or what they do not achieve. We can generalise over these sorts of

negative definitions to find a common distinction between heuristic processes and processes

that are guaranteed to produce correct answers or outcomes. I will refer to these latter as

GCO (guaranteed-correct-outcome) procedures.

GCO procedures are essentially formal operations, paradigmatically those of

mathematics or logic. For example, applying the rules of division will guarantee that you

will arrive at the correct answer to a specified division problem of arithmetic; constructing

truth-tables will guarantee a correct determination of whether a specified set of

propositions is consistent; and so on. However, GCO procedures exist beyond the paradigm

of logic or mathematics. We can easily come up with an algorithm to, say, determine

whether a lamp needs replacing, or to phone a friend. There are even algorithms for

playing tic-tac-toe which guarantee either a win or draw (Crowley and Siegler [1993]).

In general, GCO procedures necessitate the right answers, when applied correctly. In

contrast with these GCO procedures, heuristics are supposed to be procedures that

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efficiently produce outcomes or answers that may be good enough for one’s purposes, and

that may sometimes end up to be correct, but they won’t guarantee correct answers. Thus,

negative definitions of this type can be summed up as follows.

HN Heuristics are procedures that do not guarantee correct outcomes,

although they can can provide certain benefits.

I will discuss the property of providing ‘certain benefits’ in more detail when I offer my

positive characterisation below. For now we will focus on the ‘do not guarantee correct

outcomes’ part of this definition. In particular, I shall address the extent to which the

claim that heuristics are procedures that do not guarantee correct outcomes does useful

work for us as a central part of a definition of heuristics.

Let us begin by observing that, in the small number of contexts considered so far, HN

makes perfect sense—in math, logic, tic-tac-toe, and so on, we can understand heuristics as

procedures that do not guarantee correct outcomes as GCO procedures do, though they

offer certain benefits. For example, randomly selecting a limited subset of a set of

propositions and simply looking at its members to see if any contradicts any other is a

heuristic process to check the consistency of the superset of propositions; ‘always start in

the centre square’ is a heuristic for tic-tac-toe (Dunbar [1998]). Such heuristics won’t

guarantee a correct outcome, but they are at least cognitively efficient. In general, HN is

applicable in cases when there exists a GCO procedure for a given problem. Of course, the

GCO procedure need not be feasible (as when the GCO procedure cannot be practically

performed by a human (or even machine) because it is too complex, or too

time-consuming, or too taxing on cognitive resources),9 and the GCO procedure need not

9Computational complexity theorists call such intractable problems ‘NP-complete’, and the TravelingSalesman problem is the paradigm case. We may note in passing that heuristics are the only viable procedureswhen dealing with NP-complete problems. Cf. the discussion below.

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be known for a given problem, so long as there exists a GCO procedure in principle.

Notice, however, that the problems for which HN is usefully applicable are all

well-defined problems. It should be known well enough that well-defined problems have

well-defined problem-spaces, with discrete states and goals that are, or can be in principle,

known and understood. Tic-tac-toe, problems in math and logic, dialing a friend—they all

have well-defined problem-spaces. Having a well-defined problem-space is what allows for

the generation of algorithms that guarantee correct outcomes. For not only are the goals of

well-defined problems understood and known to be correct outcomes—that is, we know

precisely what a correct outcome is for these sorts of problems—additionally one can

identify definite and discrete steps by which to navigate the problem-space, proceeding

from one state to the next, so as to ultimately reach the goal state. This is what is meant

by a problem having a GCO procedure in principle—if the states and goals of a problem

are well-defined, then there will exist some procedure that will guarantee a correct

outcome, even if this requires exhaustive search and evaluation of the problem-space (even

if the problem is NP-complete; see note 9).

But here is the trouble: When faced with a well-defined problem, we are almost always

restricted to the use of heuristics in the sense of HN. To be sure, cognitive limitations or

time constraints often prevent us from carrying out a GCO procedure, or there is just no

known correct solution or no known GCO procedure (notwithstanding that these may exist

in principle). Indeed, the well-defined problems for which there are known feasible GCO

procedures are very few (Richardson [1998]). In this light, then, we may very well

understand heuristics as procedures that do not guarantee correct solutions, but in doing

so we seem to allow too much in. For when we consider real-world contexts, where time

and resource constraints are ubiquitous, engaging in GCO procedures won’t be a viable

option for a great many tasks. Thus, we come to an important problem for HN: The

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widespread claim that much of human cognition is heuristic is nearly trivially true, since

much of our cognition cannot be anything but heuristic as described by HN. I will call this

the ‘triviality problem’.

Not only are GCO procedures rarely a viable option in the real-world (when we are

faced with a well-defined problem), but in addition, well-defined problems are relatively

rare. Instead, we are commonly confronted with ill-defined problems, which have undefined

or indeterminate states and/or goals. The problem-spaces for ill-defined problems cannot

be completely or adequately known, understood, or characterised, and so there are no clear

solution paths for ill-defined problems.10 Ill-defined problems include grandiose problems

such as stabilising the current state of the economy, and coming up with a feasible policy

to reduce carbon emissions, as well as more humble problems such as deciding whether to

take a job offer, planning a party, and writing a good paper. By their very nature,

ill-defined problems preclude the possibility of GCO procedures. For the goals of these

problems are often insufficiently defined, and as a result it is unknown what a ‘correct’

outcome would be, thereby making it impossible to have a procedure that would guarantee

a correct outcome. Moreover, even if an ill-defined problem has a sufficiently defined goal,

such as determining the culprit in a murder case, the means by which one would proceed to

achieve this goal would likely still be uncertain since either the mediating states may

remain indeterminate, or we are unable to properly evaluate the steps taken (for example,

whether the work one does on the murder case brings one closer to or further from

10The distinction between well-defined and ill-defined problems goes as far back as the infancy of artificialintelligence research (see McCarthy [1956]). McCarthy’s original characterisation has been reexamined andextended by a number of researchers (most notably Reitman [1964], [1965]; Newell [1969]; Simon [1973];more recent treatments are found in Voss et al. [1983]; Shin et al. [2003]; Lynch et al. [2006]; Voss [2006];Mitrovic and Weerasinghe [2009]). It is perhaps an important task to critically analyse the concept of anill-defined problem to arrive at a fully developed account, but it is beyond the scope of this paper to providethis analysis. For those who desire a more thorough account of the distinction between ill-defined andwell-defined problems, I refer them to the works cited here.

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determining the culprit); there still would be no clear solution path.11 This situation is

particularly bad news for HN, for if there is no way to evaluate intermediate steps toward a

goal in such ill-defined contexts, then no sense can be made of heuristics being satisfactory,

reasonable, or ‘good enough’ solutions. That is, we would not know what would make a

heuristic solution satisfactory, reasonable, or ‘good enough’ in ill-defined contexts.12

Since it does not make much sense to speak of correct outcomes for many ill-defined

problems, much less processes that guarantee correct outcomes, little sense can be made of

HN in this context, in particular its claim that heuristics are procedures that do not

guarantee a correct solution. The situation would not be so bad if it were not the case that

a vast number of real-world problems humans typically face are characteristically

ill-defined. Alas, we do not live in a tic-tac-toe world. Thus, in addition to the triviality

problem cited above, HN faces what I call a ‘range problem’: ‘heuristic’ doesn’t apply to an

interesting range of cases, since we are typically confronted with ill-defined problems for

11While one may argue that there very well may be a correct way to, for example, stabilise the economy,the correct way is realised only retrospectively. If this weren’t so, many countries wouldn’t currently haveso much difficulty in stabilising their economies. Aside from this rhetoric, however, it is a fact that there isgreat uncertainty in whether measures yet to be undertaken will advance us toward the goal or away fromthe goal (as above with respect to solving a murder case). Such uncertainty is owed to the multifariouscomplexity of the problem, but it is also owed to the indeterminateness of the problem-space. Thus, onecannot know a priori what the correct solution is. But this is just the nature of ill-defined problems, viz.there are no clear solution paths. See below for more on ill-defined problems.

12We should be careful not to confuse ill-defined problems that arise from trying to solve well-definedproblems with the well-defined problems themselves. Such confusion may result when considering, for in-stance, attempting to discover a proof in mathematics or coming up with a succinct algorithm for an Internetsearch engine to retrieve specific websites. Certainly, the mathematical proof and the search algorithm arethemselves well-defined, and they are paradigmatically so, as the demonstration (or subsequent derivation)of the proof and the execution of the algorithm both have identifiable discrete goals and intermediate states.But the problem of discovering a mathematical proof or a search algorithm very well may be—and I supposeis typically—ill-defined. For even though the goal states for these problems are well-defined, there is noclear solution path since the mediating states of the problem of discovery and the problem of developmentare fuzzy and indeterminate, i.e., they have ill-defined problem-spaces. This much has been recently noted.And indeed, it is generally agreed among philosophers and cognitive psychologists that discovery in generalinvolves a measure of creativity and finesse which cannot be captured with a well-defined procedure, eventhough in some cases the object of discovery is a well-defined procedure. It was the problem of discoveringFermat’s last theorem that stalled three century’s worth of bright mathematicians, not the theorem itself;the acceptance of Wiles’ proof (after an initial correction) demonstrates this.

16

which there are no GCO procedures.

A possibility worth considering is that a deeper functional analysis of heuristics might

have it such that certain heuristics represent ill-defined problems as well-defined ones.

That is, a heuristic process might simplify a complex, ill-defined problem to a manageable

and well-defined problem. Or perhaps some independent, nonheuristic process is

responsible for representing ill-defined problems as well-defined problems, and then

heuristics are employed to solve these well-defined problems. If either of these possibilities

is the case, then it would make sense to claim that heuristics are processes that do not

guarantee correct outcomes, for they would be working within the confines of well-defined

problem-spaces for which there are (in principle) GCO procedures. This is certainly a

possibility, and many contemporary decision researchers, following the work of Simon,

agree that much of human reasoning involves search within and manipulation of

well-defined problem-spaces (Dunbar [1998]).

However, difficulties with this analysis arise when we realise that there will be always

be innumerable ways to carve up ill-defined problems into problem-spaces consisting of

discrete states. Consider, for instance, a simple, though ill-defined, problem of deciding

whether to go for a picnic. What states should the problem-space consist of, and what

would be the goal state? Should there be only two states, (i) ‘go for a picnic’ and (ii) ‘not

go for a picnic’? Or should the problem-space consist of (i) ‘go for a picnic’, (ii) ‘not go for

a picnic, but go to a restaurant instead’, and (iii) ‘not go for a picnic, but stay home

instead’?13 I need not belabour the issue here of how difficult it is to model an ill-defined

problem as a well-defined one; the problem should be familiar to the reader. The difficulty

here is similar to what is known as ‘the problem of small worlds’, introduced by L. Jimmie

Savage ([1954]; see also Shafer [1986]). The problem of small worlds concerns whether

13This example is derived from Savage’s ([1954], pp. 15–6) famous omelette example.

17

expected utility assignments will maintain the same structure, and therefore dictate the

same decisions, upon refinements of a decision-problem. As Savage recognises, there doesn’t

seem to be a plausible way to define an operationally applicable criterion to determine

whether a well-defined model maps onto the original ill-defined problem. Hence, there is no

criterion for whether or the extent to which a given well-defined model adequately captures

an ill-defined problem. In this way, we might say that representing an ill-defined problem

as a well-defined problem is itself an ill-defined problem insofar as it is indeterminate how

to represent the states and goal(s) (i.e., the correct outcome) of the problem.

I do not mean to suggest that we never simplify ill-defined problems; in fact, we

probably do this often with certain ill-defined problems.14 Of course, whether and to what

extent people actually represent ill-defined problems as well-defined problems are empirical

questions. But unless evidence would show that representing ill-defined problems as

well-defined ones is ubiquitous, there remains a large class of problems for which it is

trivial to speak of heuristics as processes that do not guarantee correct outcomes.15

3 A Taxonomy of Heuristics

14A concern that might be raised here is that rational decision making under uncertainty may not be bestdescribed in terms of ill-defined problems. For example, many Bayesians and game theoreticians conceivedecision making problems under uncertainty as well-defined problems with definite, well-defined, rationalsolutions. Nevertheless, even though the formal apparatus of Bayesianism or game theory impose a well-defined problem-space on an ill-defined problem, this doesn’t entail that the raw problem is itself well-defined.Given that uncertainty (or what we might call ‘unknown risk’) is an inherent feature of such raw problems,their problem-spaces are necessarily ill-defined. Cf. discussion in note 12. In fact it is arguable that Bayesiansand game theoreticians represent ill-defined problems as well-defined ones just because doing so allows forformal analysis on what otherwise would be an unanalyzable problem. The reader is referred to the workscited in note 10 for further clarification on the nature of ill-defined problems. See also the discussion above.

15Another negative definition implicitly suggested by some authors is that heuristics are procedures thatdo not optimise (though they can result in good outcomes) (see Carruthers [2006]; Fodor [2008]; Gigerenzerand Goldstein [1996]; Savage [1954]; Simon [1957]; von Neumann and Morgenstern [1944]). We may take thisas a special case of HN if we understand optimisation as a ‘correct outcome’. Yet optimisation procedures areusually understood not to aim at guaranteeing correct outcomes, but at maximising some value, traditionallyexpected utility. Optimisation procedures take into account problems for which there are in principle noGCOs or GCO procedures. Nevertheless, most of what I said against HN can be applied to this negativeheuristics-as-not-optimising definition, and I will refrain from rehearsing the range and triviality problems.

18

We have now considered several problems with some attempted or implicit definitions of

‘heuristic’. I will now turn to the task of offering a more adequate account of the term by

highlighting some features of heuristics that are important for theorising about cognition

generally. In undertaking this task, I draw a number of distinctions in order to give a

taxonomy of different kinds of heuristics. This will be helpful to identify some of the

important properties of heuristics, as well as to make sense of various research programmes

on heuristics. This will also serve to eventually focus in on a certain class of heuristics

found in the taxonomy—a class that is distinctively cognitive. It is this cognitive class of

heuristics that the characterisation of ‘heuristic’ developed in section 4 will apply to.

3.1 Stimulus-driven vs. heuristic

The first distinction I make is between stimulus-driven behaviour and heuristic-produced

behaviour. By stimulus-driven behaviour I do not intend to refer to the behaviourist idea

of stimulus-response that takes the mind to be a black box to remain unanalysed. Rather, I

mean to refer to some unspecified theory that takes a stimulus to be the cause, in a

coarse-grained fashion, of a response. By heuristic-produced behaviour, on the other hand,

I mean behaviour (including cognitive behaviour) that is brought about or caused by the

operation of some heuristic. Consider, for example, some heuristics found in the literature:

(1) In chess, consider first those moves that remove or protect pieces under

attack. (Simon et al. [1967])

(2) Probabilities are evaluated by the degree to which one thing or event is

representative of (resembles) another; the higher the representativeness

(resemblance) the higher the probability estimation. (Tversky and

Kahneman [1974])

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These heuristics, which may be taken as paradigm cases of heuristics, are not mere

stimulus-driven operations. Rather, they are relatively more complex operations involving

relatively more complex representations. Specifically, these heuristics are conceptual

operations, involving conceptual representations. To put it another way, these heuristics

are concept-mediated.16 In contrast, stimulus-driven behaviour does not implicate

conceptual representations, since the stimulus is supposed to be the cause (in a

coarse-grained way) of the response. As a paradigm example, we might take a case of

shuddering upon hearing an unexpected loud noise—it is unlikely that the loud noise is

conceptualised, and thus conceptual representations would have no role in producing the

shudder response; it is simply a brute reaction or reflex.

The distinction between heuristic-produced and stimulus-driven behaviour may seem

obvious, but it is an important distinction to make, especially in light of some of

Gigerenzer’s recent work. Gigerenzer ([2007], [2008b]) has speculated that some nonhuman

animal behaviour can be understood in terms of heuristics. According to Hutchinson and

Gigerenzer ([2005]), behavioural biologists have studied ‘rules of thumb’ since the middle of

the twentieth century, where rules of thumb describe some animal behaviour through

simple rules that largely appear to be innate. So, for instance, the manner in which the

16I adopt here the common view that concepts are, qua constituents of thought, complex mental entitiesthat participate in a complex system of representations. That is, I envision that concepts are structuredrepresentations. And though I remain neutral on a specific theory of concepts (if Machery ([2009]) is right,then there is a plurality of scientific entities we call concepts), we might take Jesse Prinz’ ([2002]) theory of‘proxytypes’ as (at least roughly) representative of the sort of structure I envision concepts to have. Theproxytype theory allows for a rich range of representations, from perceptual representations to more abstractones, to constitute conceptual structure. However, I do not wish to simply subscribe to Prinz’ proxytypetheory, since I think he underestimates the role that other sorts of representations have in constitutingconcepts; in particular, I have in mind representations derived from knowledge of natural language (forexample, knowing that a word operates as a noun constrains the sort of thing the word refers to). (Cf.Viger [2006].) Whatever the details may be of an appropriate theory of concepts, what is important for thepresent paper is that concepts be understood as complex structures that are at least partly constituted by arange of representations that cluster in cognition to form the concept in question. (See below for discussionon what makes a concept cognitive rather than perceptual, if a concept can be constituted by perceptualrepresentations.)

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wasp Polistes dominulus constructs its nest dictates that there are a possible 155 different

hexagonal arrangements. However, only eighteen arrangements are ever observed, and the

eighteen arrangements appear to follow a rule of thumb ‘in which the wasp places each cell

at the site where the sum of the ages of the existing walls is greatest’ (Hutchinson and

Gigerenzer [2005], p. 103). Another example: If there are two light sources in a copepod’s

environment, it will follow ‘a trajectory as if it were pulled toward each source with a force

proportional to source intensitydistance2

’. Yet behavioural biologists explain this seemingly complex

behaviour by a simple rule of thumb that says that the copepod ‘adjusts its orientation so

as to maximise the amount of light falling on [its] flat eye’ (Hutchinson and Gigerenzer

[2005], p. 103). Hutchinson and Gigerenzer claim that such rules of thumb ‘correspond

roughly’ (Hutchinson and Gigerenzer [2005], p. 98) to heuristics, though in other works

Gigerenzer appears to make the stronger claim that ‘rule of thumb’ is synonymous with

‘heuristic’ (Gigerenzer [2007], [2008b]; Gigerenzer and Gaissmaier [2011]). Gigerenzer

([2007]) goes on to explain that many other animal behaviours can be understood as being

the result of following rules of thumb or heuristics.17

However, given the distinction made here between stimulus-driven and

heuristic-produced behaviour, Gigerenzer’s belief that such animal behaviours are the result

of following heuristics may be misguided. This certainly appears to be the case with respect

to the copepod example—it is more likely that copepods are guided by stimulus-driven

mechanisms rather than heuristics; it is doubtful that copepods have the wherewithal to

possess or develop any concepts, let alone representational systems or mechanisms.

Perhaps stimulus-driven behaviour is best characterised as merely satisfying a rule, or

17For example, Gigerenzer ([2007]) believes that birds of paradise mate selection behaviour can be explainedas the females following the heuristic ‘Look over a sample of males, and go for the one with the longest tail’;Gigerenzer also claims that aggressor-assessment of deer stags follow a pattern of sequential reasoning, whichcan be described by a heuristic to the effect of ‘Use deepness of roar to estimate the size of rival first; useappearance afterward’.

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conforming behaviour to a rule. As Gigerenzer’s examples illustrate, satisfying a rule may

give the appearance that the behaviour is produced by a heuristic, but such

stimulus-driven behaviours do not involve a rule as a causal ingredient.18 We might say

that merely satisfying a rule is not sufficient for heuristic-produced behaviour. (I shall say

more on satisfying rules below.)19

It is interesting to note that some heuristics may importantly involve stimulus-driven

responses.20 Consider for instance Gigerenzer’s gaze heuristic:

(3) (i) Visually fixate on a moving object; (ii) move toward the object; (iii)

adjust your speed such that the angle of your gaze remains constant.

(Gigerenzer [2001])

According to Gigerenzer ([2007]), this heuristic appears to be used by baseball players

when they catch fly-balls, as well as by airplane pilots and boaters when they want to avoid

collisions (when one wants to avoid a collision, one uses the gaze heuristic to adjust one’s

speed to ensure that one doesn’t meet the object in question). Gigerenzer also claims that

birds, fish, flies, and other creatures use the gaze heuristic to catch prey. Now, it is difficult

18Many of Gigerenzer’s other assertions about animals following heuristics (see note 17) are likewise throwninto doubt, for the behaviour in question may be stimulus-driven. But I haven’t given here any conclusiveargument or proof that the animal behaviours in question aren’t heuristic as I understand the term here (i.e.,that the behaviour isn’t concept-mediated). Whether such behaviour invokes conceptual representations, andwhether animals invoke rules as a causal ingredient in their behaviour, are empirical matters. The point hereis just an exercise in drawing a needed distinction between stimulus-driven behaviour and heuristic-producedbehaviour.

19I suppose that some might wish to claim that what I’m calling stimulus-driven behaviour may never-theless satisfy a heuristic rule, and that in this way stimulus-driven behaviour still can be characterisedas heuristic in nature. This move should be resisted, however, since any stimulus-driven behaviour can becharacterised as satisfying some arbitrary rule or other. For example, the shudder response to a loud noisecan be characterised as satisfying the rule ‘Shudder upon hearing an unexpected loud noise’, or ‘Display fearbehaviour when confronted with unexpected intense auditory input’, or a variety of others. I take this to bean unacceptable result because the role such rules would have in stimulus-driven behaviour is unclear, andby all lights vacuous.

20Thanks to an anonymous referee for some insightful comments which led me to the present discussion,as well as some significant discussion in the following subsection.

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to determine whether the gaze heuristic is inherently concept-mediated. While it is almost

certain that a human can use (3) conceptually, such as when a novice baseball player is

learning how to catch fly-balls, fish and insects arguably don’t possess the appropriate

conceptual wherewithal to likewise deploy (3). In this way, the cases of fish and insects

seem more like the copepod case of stimulus-driven behaviour. However, if Gigerenzer is

correct that (3) is the mechanism underlying the behaviour of baseball players and insects

alike, and that the gaze heuristic is indeed a heuristic, then it appears that my proposal

that heuristics are concept-mediated is thrown into question. In response, I should like to

emphasise that the distinction between stimulus-driven and heuristic-produced behaviour

should not be taken in the mutually exclusive sense. Rather, I make the distinction to

exclude mere stimulus-driven behaviour from (what I take to be) a useful and robust

account of heuristics. My claim is just that, if a behaviour is heuristic-produced, then the

behaviour is produced by a concept-mediated mechanism. I’m not making the further

claim that no stimulus-driven mechanisms can be involved. Furthermore, though it is

possible for the gaze heuristic to be concept-mediated, as in the case of the novice baseball

player, it need not. This seems to be obvious from the fish and insect cases, but also from

the fact that skill development can often ingrain behaviours to the extent that behaviour

becomes stimulus-driven. In light of these remarks, I submit that the gaze heuristic, insofar

as it is a heuristic, is a special sort of heuristic. This special sort of heuristic is captured by

the distinction I make in the following subsection.

3.2 Perceptual vs. cognitive heuristics

An additional important distinction to make is between perceptual heuristics and cognitive

heuristics. Perceptual psychologists who subscribe to the perceptual heuristics approach to

vision or speech perception believe that the human perceptual system is too deficient to

23

fully compute perceptual information coming in from the environment; or that the

perceptual information in the environment is too vague to produce a certainly veridical

output (Braunstein [1994]). And so, it is claimed, the human perceptual system relies on

heuristics to make approximations. An example of a visual perceptual heuristic is:

(4) If a repetitive texture gradually and uniformly changes scale, then

interpret the scale change as a depth change. (Feldman [1999], p. 215)

Although such perceptual heuristics are often expressed in conceptual terms, they are

nonconceptual in operation.

Now, there has been a recent movement in psychology and philosophical psychology,

commonly referred to as ‘embodied cognition’ or ‘situated conceptualisation’ (see Barsalou

[2005]), which understands conceptual processing as ‘grounded in’ the perceptual systems

and involving the (re)activation of perceptual representational processing (cf. note 16). In

light of this movement, which enjoys considerable empirical support, I don’t wish to make

any substantial claims about the relation between perception and cognition, or between the

perceptual systems of the brain and the conceptual systems. However, I believe that the

distinction with respect to perceptual and cognitive heuristics is useful, and indeed needed

in order to narrow in on certain cognitive kinds commonly discussed in the psychology and

philosophy literatures. Thus, I propose the following: Perceptual heuristics can be

understood to use only information resulting from and maintained by occurrent distal and

proximal stimuli, whereas the information used by cognitive heuristics does not rely on

occurrent stimuli.21 If this distinction is granted, then perceptual heuristics constitute a

special class of heuristics insofar as they are mediated by perceptual representations rather

21This account enjoys inspiration from a talk given by Jacob Beck at The 9th International Symposiumof Cognition, Logic and Communication: Perception and Concepts, in Riga, Latvia, May 2013. I make noclaim that Beck would be pleased with my gloss here.

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than by concepts. In this way, (4) will constitute a perceptual heuristic but not a

conceptual (cognitive) heuristic. On the other hand, (1) and (2), given as paradigm cases

of heuristics above, are not perceptual heuristics. Rather, they are cognitive in nature;

they are cognitive heuristics.

Furthermore, we might now understand that (3) the gaze heuristic is not so much a

cognitive heuristic as it is a perceptual heuristic, despite Gigerenzer’s seeming claims to the

contrary. We might characterise the gaze heuristic more precisely as a percept-motor

heuristic, since it also involves online adjustments to bodily motion. In any case, as a

heuristic for object tracking, occurrent distal and proximal stimuli are required. This leaves

open the possibility for nonhuman animals that lack the appropriate conceptual

wherewithal to employ the gaze heuristic as a noncognitive percept-motor heuristic. So, on

the present account, the gaze heuristic need not be a cognitive heuristic. I say ‘need not

be’ because, as intimated above, it is possible for humans to use such a heuristic

cognitively (i.e., conceptually).

Before continuing on, it would be instructive to say something about the interesting

fact that nonhuman animals possess and use some of the same heuristics as humans. This

appears to be true of the gaze heuristic, and it may be true of others. If I were to guess, I

would suppose that the shared heuristics among human and nonhuman species are mainly

perceptual in nature. The motivation for this supposition has to do with having

evolutionary problems in common, along with possessing similar (though not always

identical) perceptual systems to solve those problems. In general, I believe we can point to

certain core systems or core capacities to explain at least some of the similarities and

differences between the sorts of heuristics species possess and use.22 Humans and a great

22The term ‘core capacities’ is used by Gigerenzer to explain how heuristics work (Gigerenzer and Gaiss-maier [2011]), and in some respects the present account is similar to Gigerenzer’s. He claims that heuristicsexploit core capacities. However, in contrast, I prefer to think of heuristics as operations employed by core

25

many nonhuman species have core visual systems, and object-tracking is a common

problem; so it seems sensible to assume that similar solutions were arrived at. On the other

hand, humans don’t always share core capacities with nonhuman species. Ants have core

systems and capacities to lay and recognise pheromone trails, and they may therefore

possess and utilise heuristics to track pheromone tails. It would be impossible for humans

to possess these sorts of heuristics since humans lack the requisite core capacities. Such

pheromone heuristics, if any there are, would be sorts of perceptual heuristics in the sense

described above insofar as they are not concept-mediated. Of course, it is possible that

humans and nonhumans share some cognitive heuristics, but in such cases similar cognitive

(conceptual) systems would be deployed. Shared conceptual systems across species, I

suppose, would be less common than shared or similar core perceptual capacities with

perceptual heuristics. At the same time, if all of this is correct, we might be able to learn

something about the perceptual and conceptual representational systems of nonhuman

animals if and when they deploy similar heuristics as humans.

3.3 Computational vs. cognitive heuristics

Some may take issue with the contention that heuristics exploit either conceptual or

perceptual representations by pointing out, for instance, that many heuristics developed by

computer programmers operate within systems that (arguably) do not possess, and

(arguably) are not capable of possessing, conceptual or perceptual

representations—representations of the sort we are wont to ascribe to cognitive systems.

To respond to this objection, we might draw a further distinction between cognitive

heuristics and what I will call computational heuristics.

I don’t want to make a big fuss about this proposed distinction. The point of it is to

capacities.

26

home-in on the sorts of operations that are distinctly cognitive, so that we might be able to

identify a certain class of heuristics as a cognitive kind. This latter task is important if, as

discussed in section 1, cognitive science is in the business of discovering and studying the

kinds within its domain. In so doing, I suggest that we set aside operations that may be

labeled ‘heuristic’ but do not require any sort of cognition—conceptual or perceptual—to

execute. A case in point is heuristics, with varying complexities, that facilitate economical

search within decision-trees. Nothing cognitive need be involved in such a decision-tree

search. Although cognitive heuristics may very well be computational in nature insofar as

the computational theory of mind holds, the way I am using ‘computational’ here is to refer

simply to processes that do not operate within a representational cognitive architecture.23

Notice that computational heuristics are still heuristics—they are just of a sort

different from cognitive heuristics, just as perceptual heuristics are of a different sort. And

it is an open matter whether and to what extent representational, nonheuristic cognitive

processes involve computational heuristics. However, the main point to the present

distinction is that cognitive heuristics, as I propose to understand them, are processes that

operate within a conceptual representational cognitive architecture.

3.4 Methodological vs. inferential heuristics

Finally, I make a distinction between what I will call methodological heuristics and

inferential heuristics. This distinction falls within the category of cognitive heuristics. The

23Perhaps the proper relation between computational heuristics and cognitive heuristics is one in whichthe latter is a subset of the former, rather than an oppositional relation. But the purpose of making thedistinction doesn’t hinge on the proper relation between the two. All that matters is that we identifycognitive heuristics as those that involve a representational cognitive system. Thus, even when what isbest called a cognitive heuristic is employed in a nonrepresentational, noncognitive system, I would call ita computational heuristic in that setting. An example: Gigerenzer’s take the best heuristic (see below)has been successfully implemented for automated literature search in libraries (Lee et al. [2002]). Whenimplemented in a computer program for literature search in libraries, take the best is a computationalheuristic; when employed by a human, the heuristic is cognitive.

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etymological understanding of the term ‘heuristic’ concerns methods of discovery. It was in

this sense that George Polya ([1957]) employed the term to refer to the endeavour of

studying the strategies and processes typically useful for solving problems. Some of his

strategies included:

(5) Draw a diagram when trying to solve a problem.

(6) If you can’t solve a problem right away, try an indirect proof.

(7) Try to restate the problem in different terms.

(8) Assume you have a solution and work backwards.

(9) Find a related problem that has been solved before, and try to use its

result or method.

Heuristics, in this tradition, are methodological devices for learning and

problem-solving. It is in this sense that the use of models and analogies are heuristic

devices to help us learn or understand something about our world, and that the techniques

offered by Polya are heuristic aids in solving problems. This is what I intend to refer to by

methodological heuristics. As such, methodological heuristics are what concern

philosophers of science and cognitive scientists who are interested in creative thought, the

process of discovery, and the construction and improvement of theories in science (for

example, Popper [1959]; Lakatos [1963–4]; Wimsatt [2007]; Bechtel and Richardson [2010]).

However, a different meaning of ‘heuristic’ was invoked in psychology with the Gestalt

theorists, and later with Simon’s notion of ‘satisficing’. This meaning was popularised in

the 1970s by the work of Daniel Kahneman and Amos Tversky (see Kahneman et al.

[1982]; Kahneman and Tversky [1973]; Tversky and Kahneman [1974]). The heuristics

studied by Kahneman and Tversky (and others such as Gigerenzer, and Simon to some

28

extent, although both Gigerenzer and Simon had interests in methodological heuristics) are

not precisely the methods of discovery and invention intimated by the term’s etymology.

The important distinction to recognise here is between the respective domains of use, and

their respective functions in our cognitive lives. As tools or devices for discovery and

problem-solving, methodological heuristics are aids to learning and understanding. In

contrast, the heuristics that are of interest to Kahneman and Tversky (and certain other

psychologists) are principles that guide judgement and inference. Thus, these latter are

what I call inferential heuristics. Inferential heuristics are not about learning or

understanding per se, but serve to facilitate judgements, inferences, and decision-making.

In a certain sense, inferential heuristics may be understood as special cases of

methodological heuristics, where inferential heuristics aid in the discovery of a solution to a

problem by providing the appropriate judgements and inferences. Nevertheless, inferential

heuristics remain distinct in kind from methodological heuristics insofar as either serves

distinct cognitive functions. Moreover, we can distinguish inferential heuristics from

methodological heuristics by making some generalisations. Inferential heuristics are often

epistemically opaque—people often employ these heuristics without knowing that they do

so, and without knowing the nature of these heuristics (that is, absent of a psychologist

informing one of such things). Methodological heuristics, on the other hand, are generally

epistemically transparent—these methods are more or less easily identified; we often

consciously and deliberately employ them; their usefulness is usually known; and, because

of this, an individual is able to compare and manipulate them (and all this without a

psychologist informing one of such things). Furthermore, methodological heuristics are

typically cultivated by experience and therefore vary between individuals, whereas

inferential heuristics can be to a large extent immune to experience and very common

29

among everyone, and some even may be innate.24 For example,

(9) Find a related problem that has been solved before, and try to use its

result or method,

is a technique that one acquires by working through many problems and drawing abstract

principles, whereas the representativeness heuristic

(2) Probabilities are evaluated by the degree to which one thing or event is

representative of (resembles) another; the higher the representativeness

(resemblance) the higher the probability estimation;

and the availability heuristic

(10) The frequency of a class or the probability of an event is assessed

according to the ease with which instances or associations can be brought

to mind (Tversky and Kahneman [1974]);

are pervasive, as those in the ‘heuristics and biases’ tradition have shown, and are not

cultivated or developed through conscious, intentional experience; in fact they are in many

respects immune to conscious, intentional revision.

This is not to say that inferential heuristics cannot be instantiated in higher-order

cognition, however. For instance, it is possible that one can learn and consciously employ

the availability or representativeness heuristic (cf. the discussion on the gaze heuristic

above). Moreover, it may not always be clear whether a given heuristic falls in the

methodological or inference category. That there are fuzzy cases, however, does not bear

24I use the qualifiers ‘often’ and ‘generally’ and ‘typically’ because there will undoubtedly be exceptions.The exceptions, I suppose, can contribute to our understanding of the natures of methodological and infer-ential heuristics.

30

negatively on the methodological-inferential distinction drawn here. Indeed, fuzzy cases

should not come as a surprise since it is not uncommon for us to learn something about the

world while we make inferences, nor is it uncommon that the very act of making a

judgement solves a problem. Nevertheless, the functional distinction between

methodological and inferential heuristics can be maintained so long as the functional role of

the heuristic can be determined.

3.5 Summary of distinctions

Let us briefly pause here to summarise the distinctions presented thus far.

Heuristic-produced behaviour are to be distinguished from stimulus-driven behaviour.

Moreover, there are many kinds of heuristics, including (though perhaps not exhausted by)

computational, perceptual, and cognitive. And of cognitive heuristics we can identify

different sorts: methodological heuristics and inferential heuristics. Some of these heuristics

may overlap or relate in ways that I haven’t accounted for here. Nevertheless, we are

presented with a working taxonomy to help us to understand past and current research and

arguments concerning heuristics, and to frame and guide future research and arguments.

The taxonomy is represented in Figure 1.

4 Characterising Cognitive Heuristics

Now that I have distinguished between different kinds of heuristics and discussed some of

the relations between them, I will develop a more detailed sketch of the class of cognitive

heuristics that seems to be of central interest to theorising about human cognition, namely

cognitive heuristics. Although my concern will be for cognitive heuristics in general, the

characterisation I will give will be most applicable to inferential heuristics. This will

become apparent quite quickly. However, as I proceed I will comment on how the

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Heuristics

Perceptual heuristics

Cognitive heuristics

Computational heuristics

Inferential heuristics

Methodological heuristics

Stimulus-driven behaviour

Figure 1: A taxonomy of heuristics represented as class inclusions/exclusions. I leave open thepossibility of some overlap of certain classes of heuristics.

characterisation of inferential heuristics I develop relates to methodological heuristics, as

well as to perceptual and computational heuristics. In this section, I will refer to cognitive

heuristics simply by ‘heuristics’ unless otherwise specified.

4.1 Heuristics as rules of thumb

Heuristics are almost invariably characterised as ‘rules of thumb’. So common is this

characterisation that one may even take ‘rule of thumb’ to be synonymous with ‘heuristic’

(see Pearl [1984]). (This use of ‘rule of thumb’ should not be confused with its use by

behavioural biologists which, in section 3.1 above, was described to be more associated

with stimulus-driven behaviour than with heuristic-produced behaviour.) Though I do not

want to commit to wholly endorsing this synonymity (see below), such a

rule-of-thumb-definition illuminates several central qualities of heuristics. One such quality

is that heuristics are rules of some sort. Notice however that as rules, heuristics need not

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(and perhaps should not) be understood as normative.25 Rather, as rules, heuristics are

procedures that can be specified and applied in a given situation. That is, ‘rule’, as it is

being used here, refers not to a prescriptive guide for conduct, but to a procedure that

(nonprescriptively) regulates or governs some process, or describes a method for performing

some operation (cf. Rawls [1955]).26

It would be useful here to make some distinctions with respect to the roles rules can

play in action or behaviour. It is common to differentiate between satisfying a rule and

following a rule (cf. Searle [1980]; Wittgenstein [1953], §§185–242). To satisfy a rule is

simply to behave in such a way that fits the description of the rule—merely to conform

behaviour to the rule. It is in this sense that the motion of the planets satisfy the rules

embodied by classical physics. On the other hand, following a rule implies a causal link

between the rule and some behaviour, and moreover that the rule is an intentional object.

Fodor’s recent account is particularly illuminating here: ‘following [a rule] R requires that

one’s behavior have a certain kind of etiology; roughly, that one’s intention that one’s

behavior conform with R explains (or partly explains) why it does conform to R’ (Fodor

[2008], pp. 37–8). Thus, merely satisfying a rule is not sufficient for following the rule.

Now, our concern with respect to cognitive heuristics is not so much about behaviour

as it is about reasoning.27 Let us therefore say that to satisfy a rule in reasoning is to

reason in such a way that merely conforms to or fits a description of the rule, whereas to

25Kahneman and Tversky oppose heuristics to rules (see their [1982], [1996]). But they are contrastingnormative rules with heuristics, the latter which I take here to be characterised as descriptive rules.

26Of course, there are normative matters with respect to the application of certain heuristics in certainsituations. These are matters in which Gigerenzer and his followers are engaged. They defend a view ofecological rationality, which asserts (very roughly) that a heuristic is rational in a given environment insofaras it is adaptive in that environment. My own view is that a great deal more must be said about rationalitythan what ecological rationality offers in order to make it a substantive philosophical view. But a seriousdiscussion of this matter is beyond the scope of this paper, so I set it aside here.

27Reasoning might be construed as a special case of behaviour—cognitive behaviour, as it were—in whichcase there is not much substance to this distinction. But the point of the present discussion will be preservedeither way.

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follow a rule in reasoning implies a causal role for the rule in reasoning by its being an

intentional object (cognitively represented). I suppose that in both these ways a rule can

(nonprescriptively) regulate, govern, or describe a reasoning process.

We saw above that stimulus-driven behaviour is best characterised as satisfying a rule;

and since rule-satisfying behaviour does not implicate the involvement of cognitive

representations, stimulus-driven behaviour is distinguished from heuristic-produced

behaviour. In terms recently stated, merely satisfying a rule is not sufficient for

heuristic-produced behaviour. I believe we can likewise observe that satisfying a rule in

reasoning is not sufficient for heuristic reasoning, though not because satisfying a rule in

reasoning doesn’t involve cognitive representations (indeed, I’m not sure how much sense

can be made of nonrepresentational reasoning). Rather, satisfying a rule in reasoning is not

sufficient for heuristic reasoning because some heuristic must have a causal role in a

heuristic reasoning process, otherwise we would not be able to say that the reasoning

process was in fact heuristic. To paraphrase Fodor, heuristic reasoning requires that it have

a certain kind of etiology. Nevertheless, I do not think that heuristics are necessarily rules

that are followed in reasoning, for I do not think that heuristics are necessarily represented

in cognition. Fodor ([1975], [2000], [2008]) argues that reasoning generally requires

representing the rules according to which one reasons.28 But this does not seem to be a

necessary requirement of reasoning, especially with respect to heuristics. As we saw,

inferential heuristics are often epistemically opaque, and they are pretty much automatic

and sometimes impervious to change. In any case, I see no reason why heuristics must be

intentional objects in cognition. It seems entirely plausible that they can be rules that

28More specifically, Fodor believes that acting (that is, intentional acting, as opposed to reflex or thrashingabout) requires planning, which requires deciding on a plan, which requires representing plans; on theother hand, he believes that belief fixation requires hypothesis formation and confirmation, which requiresrepresenting hypotheses.

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operate in cognition, but are neither consulted nor represented when employed. And it is

certainly not impossible for computational procedures to be executed without being

represented; even Fodor ([2008], p. 37) admits that there must be at least some rules that

are not represented in computations, e.g., those that instruct a Turing machine to move

along the tape. Thus, I propose that heuristics are plausible candidates to be

unrepresented rules in cognition, and hence that heuristics are employed, having a causal

role in reasoning, but not followed. This is not to say that being unrepresented is a

necessary condition for a rule to be heuristic. Indeed, many heuristics are explicitly

represented; this is especially true of methodological heuristics, and I believe it is obvious

that some inferential heuristics can be explicitly represented, such as when novices begin to

learn the skills of a trade. My claim, however, is that heuristics need not be, and often are

not, represented in cognition.

In light of these considerations, let me make a further distinction between, on the one

hand, satisfying a rule and following a rule, and on the other hand, acting accordance with

a rule. ‘Acting in accordance with a rule’ is sometimes meant in the same sense as

satisfying a rule, but I will suggest a special way to understand it here. By ‘acting in

accordance with a rule’, I propose to mean that a rule is guiding one’s behaviour and that

there is a causal link between the rule and the behaviour—in Fodor’s terms, the rule is

implicated in the etiology of the behaviour that accords with the rule—but the rule is not

an intentional object in cognition. In terms of reasoning, reasoning in accordance with a

rule means that the rule has a causal role in the reasoning process, but is not represented.

Notice that in this way a rule still (nonprescriptively) regulates, governs, or describes a

reasoning process.

This notion of acting in accordance with a rule is roughly what Daniel Dennett ([1991])

refers to when he talks about ‘intermediate regularities’ in systems. In ‘Real Patterns’, he

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explains intermediate regularities thus:

Philosophers have tended to ignore a variety of regularity intermediate between

the regularities of planets and other objects ‘obeying’ the laws of physics and

the regularities of rule-following (that is, rule-consulting) systems. These

intermediate regularities are those which are preserved under selection pressure:

the regularities dictated by principles of good design and hence homed in on by

self-designing systems. That is, a ‘rule of thought’ [. . . ] no more need be

explicitly represented than do the principles of aerodynamics that are honored

in the design of birds’ wings. (Dennett [1991], p. 43)

We can easily understand heuristics as such intermediate-level ‘rules of thought’ which are

happened upon throughout the course of learning, or in Dennett’s terms, throughout the

course of self-design. In fact, I am inclined to believe that inferential heuristics generally

are rules that one reasons in accordance with (as I am using the phrase), whereas

methodological heuristics are usually (though perhaps not always) followed. Whether this

is true, however, does not bear on the present point, which is that heuristics in general do

not have to be represented when employed. Let us therefore observe that:

H1 Heuristics are cognitive procedures that can be expressed as rules one

reasons in accordance with,

where ‘reasons in accordance with’ is to be understood in the special sense given here. H1

expresses the first quality of heuristics illuminated by the rule-of-thumb-definition.

Another quality of heuristics illuminated by the rule-of-thumb-definition is that a rule

of thumb is so called because a thumb can be used as a device for rough estimations;

historically, one’s thumb was likely used as a tool for rough measurements. We might take

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this observation to imply that heuristics are imprecise cognitive tools. But this is too broad

a claim, for there are many imprecise inferential procedures that we would hesitate to call

heuristic. For instance, procedures that are irrelevant to the task at hand, or that

invariantly result in disaster, are (in some sense) imprecise, but such procedures are by no

means heuristic (cf. discussion in section 2.2 above). Moreover, Gigerenzer has shown that

heuristics can sometimes outperform complex operations on certain decision-tasks. For

example, in choosing which of two cities is larger, Gigerenzer and Goldstein ([1996], [1999])

show that the recognition heuristic

(11) (i) Search among alternatives; (ii) stop search when one alternative is

recognised; (iii) choose the recognised object,

is more accurate than weighted linear models and multiple regression. Such results throw

into doubt the notion that heuristics are, or at least must be imprecise.

A natural way around this issue is to invoke satisficing. Simon ([1957]) introduced the

notion of satisficing to describe procedures that do not aim to meet the standards of

rational decision theory (or any theory of rationality governed by the dictates of logic and

probability theory), but instead aim to meet some aspiration level that is in some sense

‘good enough’ relative to the desires, interests, and goals of the agent. It is certainly

possible for a satisficing procedure to set its aspiration level commensurate with an ideal, if

one exists. However, the point of satisficing is that the bar is flexibly positioned according

to the goals and desires of the satisficer.29

29To revisit an issue discussed in section 2.2 above, one may wonder whether heuristics represent ill-definedproblems as well-defined problems, and thus whether heuristics just approximate norms. Though I don’twish to deny that this is a possibility, I don’t think that this is generally the case. We have already seen thedifficulties in representing ill-defined problems as well-defined problems. One of the key points of invokingthe notion of satisficing is that heuristics simply do not need to do any of this modelling business. Flexiblysetting goals relative to one’s needs and desires seems to be a better and more efficient strategy for finite andconstrained creatures such as ourselves than first modelling the problem and then setting about to (re)solve

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Understanding heuristics as useful procedures that do not necessarily aspire to meet

some ideal implies that heuristics are essentially satisficing procedures. Sometimes this

might not be entirely obvious. Consider two examples of inferential heuristics. The first is

Gigerenzer’s take the last heuristic,

(12) Use the cue that discriminated on the most recent problem to choose an

object; if the cue does not discriminate use the cue that discriminated the

time before last; and so on. (Gigerenzer [2001])

This may not appear at first sight to be a satisficing procedure. However, if we take

determining a method of choice to be an initial goal in a problem, a certain aspiration level

might be set with respect to this initial goal, and using the method that was used to solve

the previous problem would satisfice. Consider also Kahneman and Tversky’s availability

heuristic, which we saw above:

(10) The frequency of a class or the probability of an event is assessed according

to the ease with which instances or associations can be brought to mind.

Again, this may not appear to be a satisficing procedure, but upon closer examination we

see that this heuristic opts not to determine the actual frequency or probability of an event

via complex calculations, but instead sets an aspiration level relative to the ease with

which instances come to mind; thus, availability of instances is a ‘good enough’, i.e.,

satisficing, indicator of frequency.

Methodological heuristics, on the other hand, appear to resist the characterisation as

satisficing procedures. For example, it is difficult to see how Polya’s heuristics above (5)–(9)

it. However, even if a satisficing procedure would model an ill-defined problem as a well-defined one, so beit. The account I provide still applies, so long as the formulated well-defined goal (the ideal) need not alwayscoincide with the ideal(s) of a formal rationality theory.

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are satisficing strategies. Nevertheless, methodological heuristics are strategies that aim to

learn or understand things in the world, not by reverting to some standard operations such

as formal proofs or deductive reasoning, but by using flexible, defeasible procedures. Once

this is acknowledged, methodological heuristics begin to look like satisficing strategies, or

at least strategies arising from a need to satisfice. Polya makes this point:

We shall attain complete certainty when we shall have obtained the complete

solution, but before obtaining certainty we must often be satisfied with a more

or less plausible guess. We may need the provisional before we attain the final.

We need heuristic reasoning when we construct a strict proof as we need

scaffolding when we erect a building. (Polya [1957], p. 113)

Hence, methodological heuristics appear to be procedures that are often indispensable to

attaining complete and certain solutions; they are a provisional step that must be taken

sometimes before we reach our final goal; they are a satificing step in the problem-solving

process.

Understanding heuristics as satisficing procedures helps our characterisation in a

number of ways. First, it does justice to the evidence that heuristics can sometimes (or

often) result in good inferences, since satisficing techniques can sometimes (or often) hit

the mark, and also since what is considered ‘good enough’ can very well be close to what is

ideal. We might note that this is the sense in which computational heuristics are generally

understood in computer programming and AI research—heuristics approximate some

presumed normative ideal (such as a correct or an optimised outcome), and some heuristics

are considered better than others if they result in better approximations (Horgan and

Tienson [1998]). Furthermore, this is roughly the sense in which many perceptual heuristics

are conceived as providing approximations to an ideal, especially the perceptual heuristics

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employed by the human visual system.

Moreover, contra the HN definition, understanding heuristics as satisficing procedures

offers a positive account of what heuristics can do rather than just stating what they

cannot or do not do. This speaks to the suggestion that heuristics are useful devices for

inference and deliberation. But if a procedure fails to approximate entirely—if it produces

random results, or results that are completely off the mark—it is utterly useless, and thus

should not be considered heuristic.

Given these observations, understanding heuristics as satisficing procedures gives us a

robust notion. Let us therefore amend our characterisation thus:

H2 Heuristics are satisficing cognitive procedures that can be expressed as rules

one reasons in accordance with.

There are further essential features of heuristics that the rule-of-thumb-definition

illuminates. For what a rule of thumb lacks in precision is made up for by its convenience

and reliability. A thumb is not as accurate for measuring as markings on a rigid stick, but

it is readily accessible, easily deployed, and dependable. The same can be said of heuristics.

A heuristic is dependable because it can be counted on to produce a satisficing solution.

This is in part why heuristics are powerful inference devices, and may in part explain why

heuristics are so ubiquitous in human reasoning and inference (Gigerenzer [2001]). Yet it is

not by chance or happenstance that a heuristic succeeds or fails. Rather, heuristics process

specific kinds of information in systematic and predictable ways. This accounts for why

they work so well in certain domains, but fail miserably in others. According to some

researchers, such as Gigerenzer, heuristics are attuned to specific domains or environments

that exhibit stable informational structures, and this is what enables a heuristic to be

successful in that domain or environment. However, if the heuristic is applied in another

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domain or environment in which the same informational structures do not obtain, then the

heuristic will fail, and biases will ensue (Gigerenzer [2000], [2001], [2006]).

Heuristics are readily accessible because little cognitive resources are required to engage

them. At least this is so for inferential heuristics. We rarely, if ever, have to invest much

time and processing in thinking over whether we will employ one inferential heuristic or

another (or some other procedure). On the contrary, the empirical evidence shows that

inferential heuristics are typically available for use without the need for reflection. In fact,

many psychologists agree that some inferential heuristics are hardwired mechanisms that

are essentially automatic. (This corroborates my position that heuristics are cognitive

procedures that can be expressed as rules one reasons in accordance with.) In a similar

vein, heuristics are also easily deployed. This means that comparatively little cognitive

resources are needed in their processing, which is achieved by processing only readily

available or easily accessible information (in the environment or within the mind). That

heuristics are readily accessible and easily deployable allows other cognitive resources

(including time) to be spared, not only with respect to processing, but also with respect to

search (among information as well as procedure alternatives, if the latter occurs). This

enables swift, on-the-fly inferences, and frees up precious cognitive resources for other

tasks—virtues upon which survival generally depends. Thus, it seems that:

H3 Heuristics are satisficing cognitive procedures that can be expressed as rules

one reasons in accordance with; they require little cognitive resources for

their recruitment and execution.

Notice, however, that H3 appears to preclude methodological heuristics. This is the

point at which the present characterisation of heuristic processes departs from

methodological heuristics. Indeed, we often take our time in deciding which, if any,

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methodological heuristic to use for a given problem. Moreover, methodological heuristics

can require much cognitive resources to be recruited and executed, and as such their

deployment may not be so easy. It stands to reason that, in general, methodological

heuristics will require more cognitive resources in their deployment and processing than

inferential heuristics, since the former generally involve substantial processing and

integration of conceptual content. But these are empirical matters to be explored on some

other occasion. The present account is content with focusing on inferential heuristics that

require little cognitive resources for their deployment.

4.2 Beyond rules of thumb: exploiting information

Before being satisfied with our working characterisation of cognitive inferential heuristics

developed thus far, let us revisit and emphasise a key issue that has been pervasive in much

of the discussion. The nature of heuristics qua cognitive processes involves particular

utilisation of conceptual representations. A rule of thumb per se, on the other hand, is

merely a static, rough unit of measure, involving few, if any, representations in its

employment. In this vein, rules of thumb do not involve the same sort of information

processing that heuristics do.

To put the point another way, when one employs a heuristic, as I am characterising it

here, it tells us something about one’s conceptual wherewithal—particularly about the

content of one’s concepts and the organisation of the larger system within which one’s

concepts participate. Consider, for example, Gigerenzer’s take the best heuristic:

(13) (i) Search among cues; (ii) stop search when one cue discriminates between

two alternatives; (iii) choose the object picked out by step (ii). (Gigerenzer

[2001]; Gigerenzer and Goldstein [1999])

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When one employs this heuristic, certain beliefs are implied about the cue upon which the

choice in question was made. At the very least, we can infer that the said cue was believed

to be the ‘best’ upon which to make the choice in question. Of course, this belief need not

be explicitly represented. Rather, it could be (and probably usually is) a tacit belief, which

is embodied by one’s concepts. In this sense, that the cue is believed to be the ‘best’

implies certain things about the conceptual content of the cue as possessed by the chooser,

as well as certain things about how the cue fits within the chooser’s organised conceptual

system. Similarly, when one employs the representativeness heuristic,

(2) Probabilities are evaluated by the degree to which one thing or event is

representative of (resembles) another; the higher the representativeness

(resemblance) the higher the probability estimation;

certain (tacit) beliefs are implicated concerning what one believes about and how one

conceptualises the objects or events under evaluation, and how the representations involved

in the evaluation fit within one’s conceptual system. The upshot here is that one’s

conceptual wherewithal has a significant role in the operations of inferential heuristics.

When one employs a rule of thumb, on the other hand, one’s conceptual wherewithal

may not play much of a role at all, and therefore the use of a rule of thumb may tell us

nothing about one’s concepts or conceptual system. ‘When constructing a truth tree,

decompose those formulas that use stacking rules before those that branch’; ‘To choose a

ripe cantaloupe, press the spot on the candidate cantaloupe where it was attached to the

plant and smell it; if the spot smells like the inside of a cantaloupe, it’s probably ripe’

(Pearl [1984]); ‘Start in the centre square when beginning a game of tic-tac-toe’ (Dunbar

[1998]); ‘Measure twice, cut once’—all these are rules that can be applied willy-nilly with

very little requisite conceptual resources or content. For example, we can imagine a

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beginner at sentential logic being presented with the truth tree rule, say in a lecture, and

told to follow it. However, that this student is able to follow the rule tells us nothing

interesting about her beliefs, or more broadly about her concepts or conceptual

system—she is just doing what she is instructed to do, not really caring to think about

what she’s doing or why she’s doing it. It is in this sense that the student would be

employing the rule as a rule of thumb rather than as a heuristic.30 Importantly, what

distinguishes rules of thumb from heuristics, as I am claiming here, is the manner in which

the rule engages one’s conceptual wherewithal, and not the rule itself. In other words, the

distinction concerns not the procedure but the sort of information over which the

procedure operates. (Cf. the distinction between computational and cognitive heuristics in

section 3.3.)

A difference between rules of thumb and heuristics can also be found with respect to

the basic understanding of heuristics provided by H1, namely that heuristics can be

expressed as rules one reasons in accordance with. Let us recall here the distinction I made

between following a rule in reason and reasoning in accordance with a rule. Following a

rule in reason implies a causal link between the rule and some behaviour, and that the rule

is an intentional object in cognition; reasoning in accordance with a rule likewise implies a

causal link between the rule and some behaviour, but the rule does not have to be an

intentional object in cognition. Upon reflection we can now see that, whereas heuristics do

not have to be represented, rules of thumb usually are; that is, whereas heuristics are rules

that one reasons in accordance with, rules of thumb are typically rules that are followed.31

30Certainly, with enough experience a student eventually understands truth trees and uses the rule in anautomatic way. But this doesn’t mean that she is (once again) not caring about what she is doing or whyshe is doing it. Rather, I suppose that it is in virtue of a thorough knowledge of truth trees that the rule hasbecome embedded in the student’s conceptual system in such a way that it can be deployed unconsciously.

31On this account, it is possible that a rule starts out as a represented rule of thumb, and with enoughexperience the rule turns into a heuristic as one’s representational wherewithal plays more of a role whenusing the rule. This I believe to be plausible especially with respect to methodological heuristics.

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I therefore resist simply equating heuristics with rules of thumb. The basis for this is

ultimately that heuristics exploit concepts, and they are successful because they do so.32

Let us draw the characterisation of heuristics that the discussion has led us to:

H4 Heuristics are satisficing cognitive procedures that can be expressed as rules

one reasons in accordance with; they require little cognitive resources for

their recruitment and execution; they operate by exploiting concepts.

As with H3, this characterisation should be understood to refer only to inferential

heuristics.

It is beyond the scope of this paper to offer an account of how heuristics are supposed

to exploit concepts.33 Nevertheless, the purpose of introducing this aspect to the

characterisation of inferential heuristics is to emphasise the central importance of

understanding inferential heuristics as essentially conceptual processes. Not only does this

corroborate the distinctions I made throughout section 3 between cognitive heuristics and

other sorts of heuristics; in addition, as I had discussed at the beginning of this subsection,

an important feature of inferential heuristics is that they allow us to infer something about

32This is similar to Gigerenzer’s conception of heuristics (see especially Gigerenzer [2000], [2001], [2008a],[2008b]; Gigerenzer and Todd [1999]). But there are important differences between Gigerenzer’s views andmy own. For instance, Gigerenzer does not make the distinctions I do between kinds of heuristics, as evincedby his confounding what I call stimulus-driven and heuristic-produced behaviour. Further, Gigerenzer doesnot develop an understanding of heuristics as exploiting concepts, as I am presently doing. Finally, whileGigerenzer asserts that heuristics operate on little information, I emphasise that heuristics generally relyon (though maybe not compute) generous amounts of information (cf. Sterelny [2004], [2006]), which onmy account is tacitly or implicitly embodied within one’s representational structures and overall conceptualsystem. See note 33.

33To be more precise, I maintain that inferential heuristics exploit, not concepts per se, but informationembodied by one’s conceptual system. In brief and rough form, here is how I envision such an account to go:When presented with a cognitive task, a set of conceptual representations are activated or primed, amongwhich associational connections exist. These connections embody a rich source of implicit (putative) knowl-edge concerning one’s concepts—their content and organisation—as mentioned above. More specifically,they implicitly embody higher-order information (or knowledge) about one’s concepts. Heuristics exploitsuch metainformation by operating over the relations that exist among one’s concepts. (Cf. Clark [2002].)This account is admittedly incomplete as stated here; a full development will have to wait for some otheroccasion.

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the content of one’s concepts and the organisation of the larger system within which one’s

concepts participate. This latter feature is interesting in itself, but it also indicates the sort

of empirical research that can be undertaken with respect to inferential heuristics and

conceptual cognition. For example, we might be able to design experiments that would

reveal information about one’s concepts based on the sorts of heuristics employed;

conversely, we might be able to predict and manipulate the sorts of heuristics employed if

we have requisitely garnered information about one’s concepts. Such research is made

possible on the present account of inferential heuristics, and it illustrates the extent to

which we can conceive heuristics as scientific kinds, as discussed in section 1.34 These are

virtues of H4.

At the same time, H4 captures what seems to be important features of certain

heuristics discussed in philosophy, psychology, and the other disciplines of cognitive science,

while being precise enough to pick out a specific kind of cognitive process. The

characterisation may therefore be used to help us understand a broad but distinct range of

34One might suggest that things might not be so neat as this. The objection is that, there are indefinitelymany ways to specify the rules that implicitly characterise a cognitive system, and this would make it difficult,if not impossible, to determine what concepts a heuristic-using system has. For instance, we might have tworules: ‘Do x if y, unless it is before January 1, 2000, in which case do z’ and ‘Do x if y, unless it is beforeJanuary 1, 2000, in which case do w’. These rules are equivalent for systems that operate only after January1, 2000, and so we wouldn’t know what concepts to attribute to these systems. (Thanks to an anonymousreferee for raising this objection along with the example.) I have two responses to this objection. (1) Giventhat the rules are equivalent for heuristic-using systems operating only after January 1, 2000, and given thatit is in fact after that date, the difference between the rules (and between the corresponding concepts) isa difference that doesn’t make a difference, so there is no need to worry about it. On the other hand, ifit were presently before January 1, 2000 (or if the rules incorporated the date of January 1, 2050), thenthere would be a difference, and this difference would allow us to distinguish between concepts possessedby systems employing either rule. And this is a good thing. (2) Furthermore, it is actually a boon for thepresent account of heuristics that there is confusion over what concepts a heuristic-using system possessesin the face of indefinitely many ways to specify the rules that implicitly characterise a cognitive system.For it indicates ways to empirically test the account and its implications; we can design empirical tests todetermine what rules a system actually uses, and conversely what concepts the system possesses. That twoheuristic-using systems can each behave similarly and yet possess different concepts for heuristics to exploitis an interesting and substantial fact that an adequate characterisation of ‘heuristic’ should accommodate.Fortunately, the present characterisation does this.

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cognitive phenomena, and thereby make clear sense of certain psychological theories of

reasoning, inference, and decision-making, as well as of certain philosophical debates

concerning reason and rationality. Heuristics are supposed to be ubiquitous in human

cognition, and so coming this much closer to understanding the nature of heuristic

processes significantly contributes to understanding the nature of the mind in general.

5 Concluding Remarks

Let us briefly review what has been achieved in this paper. We started with a vague

understanding of what ‘heuristic’ means and what heuristics are. With the motivation of

clarifying the notion of ‘heuristic’ in order to advance research and investigations in

philosophy and cognitive science generally, I considered a perfunctory negative account:

(HN) Heuristics are procedures that do not guarantee correct outcomes. I argued that this

account is unsatisfactory, since it either fails to sensibly apply to a range of important

cases of practical cognition, or it trivialises interesting features of cognition. In this way, I

contend that negative definitions such as HN are not useful for the kinds of phenomena

that we are generally interested in. Following this, I drew a number of distinctions between

different kinds of heuristics, narrowing in on a cluster of properties to offer a positive

account; the rule-of-thumb analogy proved most helpful for this purpose. The end result

was a working characterisation of inferential heuristics: (H4) Heuristics are satisficing

cognitive procedures that can be expressed as rules one reasons in accordance with; they

require little cognitive resources for their recruitment and execution; they operate by

exploiting concepts.

This account is useful and interesting for investigating several issues in philosophy and

psychology, as it provides an adequate account of a cognitive kind within the domain of

cognitive science. And this cognitive kind can be seen to have a clear place and role in

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various scientific theories, which makes it (what I had called in section 1) a scientific kind.

To be sure, each property in the cluster—satisficing, being rules, using of little cognitive

resources, and exploiting concepts—makes a substantial claim about inferential heuristics

and can be easily understood within our psychological theories. For example, the dual

process theory which is popular these days (Evans and Frankish [2009]; Kahneman [2011])

contends (roughly) that a cognitive process can be either implicit, automatic, and

unconscious (type 1) or explicit, controlled, and conscious (type 2). In its infancy, this

theory posited that heuristics were generally type 1 processes (Evans [1984], [2006]).

Recently, however, the theory recognises that heuristics can be a process of either type. We

can make sense of this in terms of how inferential heuristics are characterised here: A

heuristic can be either a type 1 or type 2 process, since all that is required is that the

process be as described by H4 which cuts across these types. Along with the sort of

empirical research discussed above that can be undertaken with respect to the ways in

which inferential heuristics bear on conceptual cognition, I take this to be a positive and

reassuring result.

The present characterisation also enables us to see the respects in which the disparate

conceptions of heuristics given by different researchers and authors overlap, as well as ways

in which they come apart. For example, as was indicated above, Gigerenzer’s use of

‘heuristic’ to refer to stimulus-driven ‘rules of thumb’ of animals is precluded by the

present characterisation of H4. Moreover, we can now clearly see why other heuristics, such

as the gaze heuristic, are not of the sort of heuristics that Kahneman and Tversky were

interested in when they began their research programme in the early 1970s; Kahneman and

Tversky were interested in the cognitive heuristics referred to by H4, not perceptual

heuristics. We can also see why some heuristics, such as those proposed by Polya, are

essentially methodological devices to provide insight, and thus are of a different species

48

than the inferential heuristics Kahneman and Tversky researched. More generally, H4 helps

us to understand whether and to what extent the examples of heuristics found in the

literature are of the same sort of phenomenon that other researchers discuss. In addition,

whereas Gigerenzer ([1996]) seems to suggest that precise computational modelling is

required to scientifically study heuristics (see also Gigerenzer and Todd [1999]), the present

characterisation offers a broader account, allowing the inclusion of non-Gigerenzer-style

heuristics. All in all, we gain a better understanding of the various ways in which the term

‘heuristic’ is used by different theorists and in different disciplines.

In addition, we are presented with new and exciting research projects to pursue. For

instance, I have not adequately described how heuristics exploit concepts. I’ve provided a

brief indication in note 33 of how I envision such an account to go, but much more work

needs to be done. The hope is that we learn more about conceptual cognition in concert

with heuristic cognition. What is it about concepts that facilitate heuristic processes?

What is it about them that enable heuristics to be ‘fast and frugal’? What is it about

them that result in the systematic biases of heuristics? An investigation into these matters

can yield further insight not only into how heuristics work, but also into more fundamental

issues concerning the nature and architecture of cognition.

Acknowledgements

I would like to thank Chris Viger, Richard Samuels, Rob Stainton, John Nicholas, and

Scott Bakker for comments and discussions on earlier versions of this paper. Thanks also

to two anonymous referees whose comments and suggestions helped to improve many

aspects of the paper.

Department of Philosophy

Mount Allison University

49

63D York Street

Sackville, NB E4L 1E2

Canada

sheldonjchow@gmail.com

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