Epistemological Metaphors and the Nature of Philosophy
To appear in Metaphilosophy.
Paul Thagard and Craig Beam
Abstract. This paper examines some of the most important
metaphors and analogies that epistemologists have used to discuss
the structure and validity of knowledge. After reviewing foundational,
coherentist, and other metaphors for knowledge, we discuss the
metaphilosophical significance of the prevalence of such metaphors.
We argue that they support a view of philosophy as akin to science
rather than poetry or rhetoric.
Keywords: epistemology, metaphor, analogy, metaphilosophy,
foundations, coherence.
1. Introduction
Epistemology is the branch of philosophy concerned with the
origins, structure, methods, and validity of knowledge. In order
to theorize about the nature of knowledge, epistemologists have
used numerous metaphors and analogies, from Plato's cave to Quine's
web of belief. This paper reviews some of the most important
of these metaphors and discusses what they show about the nature
of philosophy. Metaphors are used in many realms of discourse,
ranging from poetry to political rhetoric to scientific theorizing.
We argue that epistemological metaphors are best viewed as
theoretical rather than poetic or rhetorical, so that their historical
use supports a view of philosophy as the construction of descriptive
and normative theories.
Epistemological theories can be classified as either foundational
or coherentist. Foundational theories attempt to ground knowledge
in a solid base such as sense experience (empiricism) or a priori
reasoning (rationalism). In contrast, coherentists argue that
there are no foundations for our beliefs, whose justification
derives from how well they fit together with each other. Many
of the most influential foundationalists and coherentists have
expounded and defended their theories using suggestive metaphors
and analogies. Section 2 and 3 discuss foundational and coherentist
metaphors, respectively, and section 4 examines additional epistemological
metaphors, including ones that concern the nature of philosophy
as a whole. Section 5 then discusses the metaphilosophical significance
of the prevalence of metaphor and analogy in epistemology.
We make no sharp distinction between metaphor and analogy. Mundane
metaphors such as "my job is a jail" need not involve
much of the systematic relational mapping that is the hallmark
of analogy, but fertile metaphors such as "Socrates is a
midwife" are always based on underlying analogies (Holyoak
and Thagard 1995, p. 217). Socrates is a midwife because his
helping people to bring forth ideas is structurally similar to
a midwife's helping mothers to deliver babies. Saying that knowledge
has foundations is a metaphorical claim based on an analogy that
we now explain.
2. Foundational Metaphors
The Oxford English Dictionary (second edition) defines
a foundation as "the solid ground or base (natural or built
up) on which an edifice or other structure is erected".
Many philosophers have sought a ground or base on which knowledge
could be erected. To say that knowledge has or needs a foundation
is to use a metaphor based on a systematic analogy between the
development of knowledge and the construction of a building.
Descartes (1984, vol. 2, p. 366) explicitly endorses this analogy:
Throughout my writings I have made it clear that my method imitates
that of the architect. When an architect wants to build a house
which is stable on ground where there is a sandy topsoil over
underlying rock, or clay, or some other firm base, he begins by
digging out a set of trenches from which he removes the sand,
and anything resting on or mixed in with the sand, so that he
can lay his foundations on firm soil. In the same way, I began
by taking everything that was doubtful and throwing it out, like
sand; and then, when I noticed that it is impossible to doubt
that a doubting or thinking substance exists, I took this as the
bedrock on which I could lay the foundations of my philosophy.
Just as the architect who wants to build a stable house must find
a firm base for it, so Descartes who wants to establish stable
knowledge must doubt everything in order to find a firm base for
his beliefs. This analogy involves many interconnected correspondences,
including: architect/epistemologist, house/knowledge, build/justify,
base/indubitable knowledge, and sand/dubitable beliefs. See
Newman 1999 for a discussion of Descartes' foundationalism.
Descartes (1984, vol. 2, p. 324) also used another analogy in
defending his method of doubt, responding to a critic as follows:
Suppose he had a basket full of apples, and being worried that
some of the apples were rotten, wanted to take out the rotten
ones to prevent the rot spreading. Would he not begin by tipping
the whole lot out of the basket? And would not the next step
be to cast his eye over each apple in turn, and pick up and put
back in the basket only those he saw to be sound, leaving the
others?
Like the foundation analogy, this one serves to justify Descartes'
procedure of trying to start from indubitable beliefs, which correspond
to good apples, while abandoning dubitable beliefs, which correspond
to rotten apples. A third metaphor used by Descartes (1984, vol.
1, p. 120) to expound his epistemology is that of a chain of
reasoning:
The long chains composed of very simple and easy reasonings,
which geometers customarily use to arrive at their most difficult
demonstrations, had given me occasion to suppose that all the
things which can fall under human knowledge are interconnected
in the same way.
Below we describe Peirce's critique of the conception of knowledge
as based on a chain of inference.
Like Descartes, Spinoza thought the foundation of knowledge lay
in a priori reasoning, which he exposited by analogy to Euclidean
geometry. His book Ethics
Demonstrated in Geometrical Order proceeds by definitions
and axioms that are used to justify a series of propositions,
just as Euclid proved geometrical theorems. As did Descartes,
Spinoza wanted philosophical knowledge to be as securely demonstrated
as mathematics. Similarly, Leibniz thought that distinct knowledge
could be gained by the "light of nature" that provides
knowledge of innate ideas, which are like veins in marble that
wait to be uncovered (Leibniz 1981, pp. 84, 87).
Empiricist philosophers have looked for the foundation of knowledge
in sense experience rather than a priori demonstration, and have
accordingly employed a different set of metaphors. Here is John
Locke (1961, vol. 1, p. 77):
Let us then suppose the mind to be, as we say, white paper, void
of all characters, without any ideas; How comes it to be
furnished? Whence comes it by that vast store, which the busy
and boundless fancy of man has painted on it, with an almost endless
variety? Whence has it all the materials of reason and knowledge?
To this I answer, in one word, from experience: In that,
all our knowledge is founded; and from that it ultimately derives
itself. Our observation, employed either about external, sensible
objects; or about the internal operations of our minds, perceived
and reflected on by ourselves, is that, which supplies our understanding
with all the materials of thinking.
These two are the fountains of knowledge, from whence all the ideas we have, or can naturally have, do spring.
Here the main correspondences are paper/mind and writing/experience.
Implicit in the comparison is the foundational presupposition
that observation makes on the mind veridical impressions of objects.
A similar analogy was used much earlier by Aristotle, who compared
knowledge to writing on a blank tablet (Aristotle 1984, p. 683;
430a). He also said that sense experience is like the impression
that a signet-ring makes on a piece of wax (Aristotle 1984, p.
674; 424a). The quote from Locke introduces another metaphor,
in which observation and reflection are both fountains of
knowledge. The implicit analogy underlying this metaphor involves
the correspondences water/knowledge and shoots/produces.
Kant was fond of the foundation metaphor, as evident in the titles
of his books: Foundation (Grundlegung) of the Metaphysics
of Morals and Metaphysical Foundations (Anfangsgründe)
of Natural Science. Frege also used the metaphor in the title
of his Foundations (Grundlagen) of Arithmetic. Moreover,
in The Basic Laws of Arithmetic, he explicitly used it
in attacking psychologistic approaches to mathematics (Frege 1964,
p.13):
I understand by 'laws of logic' not psychological laws of takings-to-be-true,
but laws of truth. ... If being true is thus independent of being
acknowledged by somebody or other, then the laws of truth are
not psychological laws; they are boundary stones set in an eternal
foundation, which our thought can overflow, but never displace.
This passage amplifies Descartes' foundation metaphor by stressing
the permanent nature of the foundation and specifying laws of
logic as being as important as boundary stones. Similarly Husserl
(1965, pp.75-76), in his ambition to make philosophy a rigorous
science, wrote:
For with this blunt emphasis on the unscientific character of
all previous philosophy, the question immediately arises whether
philosophy is to continue envisioning the goal of being a rigorous
science, whether it can or must want to be so. ... Is it to be
a philosophical "system" in the traditional sense, like
a Minerva springing forth complete and full-panoplied from the
head of some creative genius, only in later times to be kept along
with other such Minervas in the silent museum of history? Or is
it to be a philosophical system of doctrine that, after the gigantic
preparatory work of generations, really begins from the ground
up with a foundation free of doubt and rises up like any skilful
construction, wherein stone is set upon stone, each as solid as
the other, in accord with directive insights?
Like Descartes, Spinoza, Kant, and Frege, Husserl wanted philosophical
knowledge to be an unchallengeable edifice built on an unassailable
foundation. However, not all philosophers have thought that
a foundation for knowledge is achievable or desirable, and they
have used a wealth of metaphors to outline an alternative view
of the nature of knowledge.
3. Coherence Metaphors
In 1860, Charles Peirce published an incisive attack on Cartesian
epistemology, rejecting the method of universal doubt. Peirce
criticized the idea of a chain of reasoning that Descartes derived
from mathematical proof. According to Peirce, (1958, pp. 40-41)
reasoning should be understood as a cable rather than a chain:
Philosophy ought to imitate the successful sciences in its methods,
so far as to proceed only from tangible premisses which can be
subjected to careful scrutiny, and to trust rather to the multitude
and variety of its arguments than to the conclusiveness of any
one. Its reasoning should not form a chain which is no stronger
than its weakest link, but a cable whose fibers may be ever so
slender, provided they are sufficiently numerous and intimately
connected.
The cable metaphor is a powerful antidote to the chain and foundation
metaphors that have dominated much of epistemology. What matters
is not the strength of a particular proposition, but its connections
with numerous other propositions. The metaphor that reasoning
is a cable is based on a complex analogy that involves interrelated
correspondences: fiber/beliefs, cable/set of interconnected
beliefs, and strength of cable/validity of knowledge. These
elements are causally related, in that just as the number and
interconnection of fibers is what makes a cable strong, the number
and interconnection of beliefs is what makes them justified.
Justification is then a matter of coherence rather than foundations.
In the twentieth century, the most influential coherentist metaphor
has been Otto Neurath's ship, which he used in arguing against
empiricist foundationalism based on protocol statements concerning
sense experience. In the 1930s, Neurath (1959, p. 201) wrote:
There is no way of taking conclusively established pure protocol
sentences as the starting point of the sciences. No tabula
rasa exists. We are like sailors who must rebuild their ship
on the open sea, never able to dismantle it in dry-dock and to
reconstruct it there out of the best materials. Only the metaphysical
elements can be allowed to vanish without trace. Vague linguist
conglomerations always remain in one way or another as components
of the ship.
The analogical correspondences here include: sailors/scientists,
ship components/beliefs, and ship repair/belief revision. Like
Peirce, Neurath takes scientific knowledge as canonical rather
than mathematics, where the axiomatic method suggests the possibility
of a foundational approach. But where Peirce used the cable metaphor
to challenge rationalist foundationalism, Neurath used the ship
metaphor to challenge empiricist foundationalism.
Neurath's metaphor was popularized by W. V. O. Quine (1960, pp.
3-4); "Neurath has likened science to a boat which, if we
are to rebuild it, we must rebuild plank by plank while staying
afloat in it. The philosopher and the scientist are in the same
boat. Our boat stays afloat because at each alteration we keep
the bulk of it intact as a going concern." In developing
his critique of the analytic-synthetic distinction, Quine (1963,
p. 42) used a series of metaphors. The totality of our knowledge
is "a man-made fabric which impinges on experience only along
the edges. Or, to change the figure, total science is like a
field of force whose boundary conditions are experience."
Quine and Ullian (1970) called their book on argumentation The
Web of Belief, using another metaphor that suggests that knowledge
is a matter of multiple interconnections rather than foundations.
They explain belief revision by analogy to what automobile mechanics
do (Quine and Ullian 1970, p. 8):
Often in assessing beliefs we do best to assess several in combination.
A very accomplished mechanic might be able to tell us something
about an automobile's engine by examining its parts one by one,
each in complete isolation from the others, but it would surely
serve his purpose better to see the engine as a whole with all
the parts functioning together. So with what we believe. It is
in the light of the full body of our beliefs that candidates gain
acceptance or rejection; any independent merits of a candidate
tend to be less decisive.
Here beliefs correspond to engine parts, and the validity of a
set of beliefs depends on their all working together like the
parts of an engine.
Other epistemologists and philosophers of science have used different
metaphors to inspire a non-foundationalist picture of knowledge.
Karl Popper (1959, p. 111) wrote:
The empirical basis of objective science has thus nothing 'absolute'
about it. Science does not rest upon rock-bottom. The bold structure
of its theories rises, as it were, above a swamp. It is like a
building erected on piles. The piles are driven down from above
into the swamp, but not down to any natural or given base; and
when we cease our attempts to drive our piles into a deeper layer,
it is not because we have reached firm ground. We simply stop
when we are satisfied that they are firm enough to carry the structure,
at least for the time being.
Like foundationalists, Popper uses a building metaphor, but he
gives it an anti-foundationalist twist by denying that the base
is firm. Susan Haack (1993, ch. 4) articulates a position she
calls "foundherentism", intended as a synthesis of foundationalism
and coherentism, by comparing knowledge to crossword puzzles.
The correctness of a word depends on the correctness of all the
words with which it intersects, requiring a kind of coherence.
In moral epistemology, the dominant metaphor has been John Rawls
1971 notion of reflective equilibrium. According to Rawls,
ethical principles are justified by balancing them against ethical
intuitions, which in turn are justified by how well they fit with
ethical principles. Principles and intuitions are to be balanced
against each other until reflective equilibrium is reached. Rawls
compared this coherentist approach to ethics to the proposal of
Nelson Goodman 1965 that logical principles are not justified
a priori but rather on how well they fit with inferential practice.
Thus the most prominent current methodology in ethics and political
philosophy is based on the equilibrium metaphor and an analogy
to logical justification.
We thus have a wealth of coherentist alternatives to foundational
metaphors for knowledge: cables, ships, fabrics, fields of force,
engines, piles in swamps, crossword puzzles, and equilibria.
None of these metaphors, however, suggests a means for actually
carrying out belief revision. Foundationalists can provide specific
models of what building an epistemological system looks like by
pointing to deductive proofs in mathematics and logic, but coherentists
have historically been much vaguer about how beliefs might be
justified by their interconnections with each other.
A recent theory of explanatory coherence, however, exploits analogies
between belief systems and neural networks to develop a rigorous
computational model of coherentist belief revision. Thagard (1989,
1992, 2000) developed ECHO, a computer program that assesses beliefs
with respect to whether they are part of the best explanation
of available evidence, by analogy with artificial neural networks.
The components of such networks are artificial neurons linked
to each other by excitatory and inhibitory connections that spread
activation among the neurons. Thagard realized that such networks
could be used to compute explanatory coherence: propositions
can be represented by artificial neurons, and the compatibility
and incompatibility relations between propositions can be represented
by excitatory and inhibitory links between neurons. The degree
of activation of the neurons after they have repeatedly excited
and inhibited each other corresponds to the degree of acceptability
of the propositions that they represent. The result of the analogy
between belief revision and neuronal processing is a computational
model of explanatory coherence that has been used to simulate
many kinds of reasoning in science, law, and everyday life.
4. Other Philosophical Metaphors and Analogies
The history of philosophy contains many other metaphors and
analogies that can not be classified as either foundationalist
or coherentist. One of the most famous is Plato's cave analogy,
from book 7 of the Republic. It is too long to quote, but here
is a summary from Holyoak and Thagard (1995, pp. 169-170):
Plato used an extended analogy to try to undercut the commonsense
view that knowledge is derived from sense perception. Plato imagined
a long cave in which people spend their whole lives fettered to
one spot, unable to turn their heads. All they can see is shadows
cast upon a wall by the light of a fire burning higher up the
cave. The shadows are of various puppets and implements that,
unknown to the people in the cave, are carried in front of the
fire by others. Plato argued that the knowledge we receive from
our senses is like the beliefs that the prisoners in the cave
have about this shadow. The prisoners assume from their limited
experience that they are achieving knowledge of reality, when
in fact they are only perceiving a dull projection of the outside
world.
On the one hand, the cave analogy is an attack on empiricist foundationalism,
designed to show the weakness of sense experience as a source
of knowledge. Plato's aim, however, was not to espouse coherentism,
but rather to defend a kind of rationalist foundationalism via
the theory of forms. Two other analogies in the Republic
contributed to the same aim: the comparison of the sun and
the good, and the divided line analogy.
Although Francis Bacon wrote before Descartes and Locke, he had
a keen understanding of how knowledge requires both sense experience
and reasoning. The synthesis is summarized in this brilliant
analogy from 1620 (Bacon 1960, p. 93):
Those who have handled sciences have been either men of experiment
or men of dogmas. The men of experiment are like the ant; they
only collect and use. The reasoners resemble spiders who make
cobwebs out of their own substance. But the bee takes a middle
course. It gathers its material from the flowers of the garden
and of the field, but transforms and digests it by a power of
its own. Not unlike this is the true business of philosophy; for
it neither relies solely or chiefly on the powers of the mind,
nor does it take the matter which it gathers from natural history
and mechanical experiments, and lay it up in the memory whole
as it finds it, but lays it up in the understanding altered and
digested. Therefore from a closer and purer league between these
two faculties, the experimental and the rational (such as has
never yet been made), much may be hoped.
This passage involves a triple comparison: empiricists are like
ants, rationalists are like spiders, but sensible epistemologists
are bees who both gather food and transform it. Bacon's analogy
shows the limitations of both empiricist and rationalist foundationalism,
but it is not explicitly coherentist.
In Bacon's day, "philosophy" referred to what are now
called the natural sciences as well as philosophy. The relation
between philosophy and the sciences remains controversial, and
different metaphors are used to express different visions of it.
It is still common to refer to philosophy as the "queen
of the sciences". This metaphor dates back at least to Boethius
(1969, p. 36) in the sixth century, who personified philosophy
as a queenly figure with books in one hand and a scepter in the
other. Competitively, other fields including mathematics, politics,
and theology have been styled as the queen of the sciences. In
contrast, Aquinas described philosophy and other sciences as a
handmaiden to transcendent theology (Aquinas 1945). In
contrast, Locke (1961, vol. 1, p. xxxv) viewed his philosophical
efforts as subordinate to those of scientists such as Newton:
"It is ambition enough to be employed as an under-labourer,
in clearing ground a little, and removing some of the rubbish
that lies in the way to knowledge". Nietzsche (1966, p. 135-137)
in turn derided the idea that philosophy should be reduced to
theory of knowledge or subordinated to science. Rather, genuine
philosophers are those who vivisect the virtues and assumptions
of their age, who dare to create new values and be legislators
of the future. Our own preference is to see philosophy as neither
superior nor subordinate to natural science, but as a partner
in understanding the world. This conception is developed further
in the next section.
First we want to mention two famous metaphors for the enterprise
of philosophy as a whole. Hegel (1952, pp. 12-13) wrote:
When philosophy paints its grey in grey, then has a shape of life
grown old. By philosophy's grey in grey it cannot be rejuvenated
but only understood. The owl of Minerva spreads its wings only
with the falling of the dusk.
Minerva was the Roman goddess of wisdom, equivalent to the Greek
goddess Athena. She was associated with the owl. Hence the owl
of Minerva is a metaphor for philosophy. Hegel's point is that
philosophy understands reality only in hindsight, or that it grasps
the meaning of a particular intellectual and cultural period only
as it passes away. For Hegel, philosophy was deeply bound up with
intellectual history.
In the twentieth century, the most famous metaphor for philosophy
is probably Wittgenstein's (1968 p. 103): "What is your
aim in philosophy? To shew the fly the way out of the fly-bottle."
The point of the metaphor is clear from his previous ones:
"Philosophical problems arise when language goes on holiday"
(p. 19); "Philosophy is a battle against the bewitchment
of our intelligence by means of language" (p. 47). Both
metaphors suggest that philosophical problems arise from linguistic
confusions, so that the solution to them is comes from escaping
the confusions. Philosophy is then like a kind of therapy against
itself. On this view, philosophy is focussed on language and
operates independently of the sciences.
5. The Nature of Philosophy
We now want to consider what conclusions can be drawn from
the fact that metaphors and analogies have played such a prominent
role in epistemology. One possible conclusion is that this prominence
is a sign of philosophical weakness. In his poem, "Very
Like a Whale," Ogden Nash wrote:
One thing that literature would be greatly the better for
Would be a more restricted employment by authors of simile and
metaphor.
Is the same true of epistemology and philosophy in general?
The fact that some of the most esteemed of all philosophers, from
Plato to Quine, have employed metaphors and analogies in developing
their epistemologies suggests otherwise. We need a conception
of philosophy that explains why metaphors are valuable, not why
they should be reduced or eliminated.
One conception of epistemology that would explain the centrality
of metaphor allies philosophy with poetry and other kinds of literary
discourse. Metaphors are ubiquitous in and crucial to poetry
(Lakoff and Turner 1989). So if philosophy is a kind of poetic
discourse, we have an explanation of why metaphors are so common
in epistemology. It is obvious, however, that the aims of the
philosophers whose metaphors were quoted in sections 2-4 were
very different from the aims of most poets. Plato, Aristotle,
Bacon, Descartes, Spinoza, Leibniz, Locke, Kant, Hegel, Frege,
Husserl, Peirce, Neurath, and Quine were not mainly trying to
produce evocative language, but rather to deepen understanding
of the nature of knowledge.
A second conception of philosophy that would explain its use of
metaphor associates it with political rhetoric aimed at increasing
the power and influence of a philosopher. Rhetoricians since
Aristotle have noticed the major contribution that metaphor makes
to efforts to convince other people. And part of the reason why
epistemologists use metaphors is that they make views more appealing
to readers and listeners. Foundational and coherentist metaphors
are used to make their proponents' epistemological positions both
clearer and more appealing to their audience. However, we do
not think that the uses of metaphor in philosophy are merely
rhetorical. Epistemologists aim to convince their readers
not just for the sake of convincing them, but because they think
they have a theory of the structure and growth of knowledge that
is descriptively and prescriptively better than alternative theories.
Metaphors undoubtedly have a rhetorical role, just as they have
an evocative one, but they also have an explanatory role that
we now discuss.
We contend that philosophical uses of metaphor and analogy are
similar to scientific ones. Holyoak and Thagard (1995, ch. 8)
distinguish four different uses of analogies in science: discovery,
development, evaluation, and exposition. Analogies have contributed
to such major scientific discoveries as Darwin's theory of evolution
and Maxwell's theory of electromagnetic forces. Analogies have
also contributed to the theoretical and experimental development
of scientific ideas, for example when Darwin used the analogy
between natural and artificial selection to better understand
evolution. Moreover, Darwin and other great scientists such
as Galileo also used analogies in arguing for the acceptability
of their theories. Finally, scientists and science educators
often use analogies as part of their attempts to communicate ideas
to others.
Similarly, analogies in philosophy have contributed to the origin
and development of epistemological theories. Euclidean geometry
suggested to thinkers such as Descartes and Spinoza how they should
develop their foundationalist epistemologies. Empiricist foundationalists
took inspiration instead from wax tablets and white paper. Coherentist
epistemologists have needed metaphors such as cables, boats, crossword
puzzles, and neural networks to suggest how beliefs could be evaluated
on the basis of their fit with one another.
In science, analogies are a relatively minor part of the evaluation
of theories, which depends more on how well competing theories
explain the relevant experimental evidence (Thagard 1992). In
epistemology, however, there is not much empirical evidence directly
relevant to the assessment of theories of knowledge, so that metaphors
and analogies carry much more of the evaluative burden than occurs
in science. Because it is not clear just what foundational
and coherentist theories are supposed to explain, much of their
plausibility comes from the intuitive appeal of the competing
metaphors. Whereas a scientist can lay out the empirical arguments
for accepting a theory, philosophers adduce a variety of considerations,
both descriptive and normative, that make their epistemologies
plausible. Thus evaluation and exposition blur together more
than in scientific discourse.
Describing knowledge as a cable both helps to expound an anti-foundationalist
view and to support its credibility in making sense of human knowledge.
Richer analogies such as the neural network underpinning of
Thagard's 2000 coherence theories make for expanded credibility
by tying epistemological theories in with empirical results from
cognitive psychology and neuroscience. The result is not a reduction
of philosophy to the sciences, because epistemology includes an
essentially normative component that differentiates it from the
descriptive theories of the sciences. To expand Peirce's metaphor,
we can think of science and philosophy as two intertwined and
intermingled cables that jointly contribute to making sense of
the human condition, in both descriptive and prescriptive aspects.
In sum, the uses of metaphor and analogy in epistemology and philosophy
in general are much the same as their uses in science. Analogy
is a powerful mode of thought that is indispensable in the formation,
development, evaluation, and exposition of theories, in philosophy
as well as science. Like science, philosophy is primarily theory
development, not poetry or rhetoric, even though rhetoric and
even poetry can sometimes be displayed in both fields. Philosophy
is not the queen, handmaiden, or under-laborer of the sciences,
but rather a partner in a collaborative endeavor to understand
and improve the world.
Paul Thagard and Craig Beam
Philosophy Department, University of Waterloo, Waterloo, Ontario,
Canada N2L 3G1
pthagard@uwaterloo.ca
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