=Paper=
{{Paper
|id=Vol-1419/paper0014
|storemode=property
|title=On The Scope of Mechanistic Explanation in Cognitive Sciences
|pdfUrl=https://ceur-ws.org/Vol-1419/paper0014.pdf
|volume=Vol-1419
|dblpUrl=https://dblp.org/rec/conf/eapcogsci/RusanenL15
}}
==On The Scope of Mechanistic Explanation in Cognitive Sciences==
https://ceur-ws.org/Vol-1419/paper0014.pdf
On The Scope of Mechanistic Explanation in Cognitive Sciences
Anna-Mari Rusanen (anna-mari.rusanen@helsinki.fi)
Department of Philosophy, History, Art and Culture Studies,
PO BOX 24
00014 University of Helsinki FINLAND
Otto Lappi (otto.lappi@helsinki.fi)
Institute of Behavioural Sciences,
PO BOX 9
00014, University of Helsinki FINLAND
Abstract In what follows, we will argue that while fulfilling these
Computational explanations focus on information processing
epistemic needs is essential in computational explanation in
tasks of specific cognitive capacities. In this paper, we argue the cognitive sciences, only the last mode of explanation
that there are at least two different kinds of computational conform to the mechanists’ way of thinking what genuine
explanations; the interlevel and the intralevel ones. Moreover, mechanistic explanation is.
it will be argued that neither interlevel nor intralevel Thus, we conclude that either philosophers of cognitive
computational explanations can be subsumed under the science need to embrace non–mechanistic computational
banner of standard mechanistic explanations. In the case of explanations, or extend the scope of what counts as
interlevel explanations, the problem is the direction of
explanation, and in the case of intralevel explanations, the “mechanistic” explanation in cognitive science.
problem are the dependencies that the explanations track.
Finally, it is argued that in the context of explanation of Computational Explanations and Mechanistic
cognitive phenomena, it may be necessary to defend more Explanation
liberal and pluralistic views of explanation, which would
allow that there are also some non-mechanistic forms of Within the last ten years, a growing number of philosophers
explanation. have defended the view that computational explanations are
mechanistic explanations (Piccinini 2004; Kaplan 2011;
Keywords: computational explanation; mechanistic
explanation; computation; Marr Craver & Piccinini 2011). For example, according to
Piccinini (2004, 2006a, 2006b) computing mechanisms can
Introduction be analyzed in terms of their component parts, their
functions, and their organization. For Piccinini, a
Computational explanations focus on information computational explanation is then “a mechanistic
processing required in exhibiting specific cognitive explanation that characterizes the inputs, outputs, and
capacities, such as perception, reasoning or decision sometimes internal states of a mechanism as strings of
making. At an abstract level, these computational tasks can symbols, and it provides a rule, defined over the inputs (and
be specified as mappings from one kind of information to possibly the internal states), for generating the outputs”
another. (Piccini 2006b).
These explanations can increase our understanding of a According to this mechanistic account,
the goal of
cognitive process at least in three ways: (i) they can explain computational explanation is to characterize the functions
a certain cognitive phenomenon in terms of fundamental that are being computed (the what) and specify the
rational or mathematical principles governing the algorithms by which the system computes the function (the
information processing task faced by a system, or (ii) they how). In other words, the idea is that an information
can explain by describing the formal dependencies between processing phenomenon would be explained by giving a
certain kinds of tasks and certain kinds of information sufficiently accurate model of how hierarchical causal
processing requirements. Moreover, in many computational systems composed of component parts and their properties
accounts1 it is often assumed that (iii) computational sustain or produce the phenomenon2.
explanations can explain the phenomenon in terms of its
implementation in more primitive constituent processes.
In recent years, a number of philosophers have proposed
2
that computational explanations of cognitive phenomena Constructing an explanatory mechanistic model thus involves
could be seen as instances of mechanistic explanation mapping elements of a mechanistic model to the system of interest,
(Piccinini 2004; 2006b; Sun 2008; Kaplan, 2011; Piccinini so that the elements of the model correspond to identifiable
constituent parts with the appropriate organization and causal
& Craver 2011).
powers to sustain that organization. These explanatory models
should specify the initial and termination conditions for the
1
For instance, Piccinini 2006a,2006b, Kaplan 2011. See also mechanism, how it behaves under various kinds of interventions,
Shagrir 2010 for discussion. how it is integrated with its environment, and so on.
111
This kind of mechanistic “computational” explanations explain why and how certain principles govern the possible
track causal dependencies at the level of cognitive behavior or processes of the system.
performances. They correspond to explanations which In this sense, interlevel explanations explain the behavior
David Marr (1982) called “algorithmic” explanations. of mechanisms at the algorithmic and implementation
However, as we have argued earlier (Rusanen & Lappi levels. In such explanations, the explanans is at the “upper”
2007; Lappi & Rusanen 2011), it is not obvious, whether computational level, and the explananda are at the “lower”
this mechanistic account can be extended to cover algorithmic or performance levels. For example, if one
computational explanations in Marr´s sense3. considers, why certain synaptic change is such-and-such,
In Marr´s trichotomy, computational explanations answers are often something like “because it serves to store
specifies what are the information processing tasks, and the value of x needed in order to compute y. Or, why is the
what is computed and why. Computational explanations wiring in this ganglion such-and-such? Because it computes,
give an account of the tasks that the neurocognitive system or approximates computation of x. In other words, pheno-
performs, or problems that the cognitive system in question mena at the lower levels are explained by their
is thought to have the capacity to solve, as well as the appropriateness of the mechanism for the computational
information requirements of the tasks (Marr, 1982). tasks.
This level of explanation is also the level, whereby the Secondly, there are computational explanations, which are
appropriateness and adequacy (for the task) of mappings rather intralevel than interlevel explanations. In short, these
from representations to others are assessed (cf. Marr, 1982). explanations track formal dependencies between certain
For example, in the case of human vision, one such task kinds of information processing tasks, and they explain by
might be to faithfully construct 3D descriptions of the describing certain kinds of information processing
environment from two 2D projections. The task is specified requirements at the level of cognitive competences.
by giving the abstract set of rules that tells us what the There are different views about the nature of the formal
system does and when it performs a computation. This dependencies, which are tracked by these computational
abstract computational theory characterizes the tasks as explanations. Some take it that the dependencies can be
mappings, functions from one kind of information to described intentionally i.e. in terms of informational
another. It constitutes, in other words, a theory of content, while some other, such as Egan (1992) argues that
competence for a specific cognitive capacity - vision, computational explanations track appropriate mathematical
language, decision making etc. dependencies by specifying the mathematical input-output-
functions that is being computed. There are also some
The Interlevel and The Intralevel pluralistic views; for instance Shagrir (2010) defends the
Computational Explanations view that there are actually two different types of formal
dependencies; the “inner” and the “outer” ones. According
It is important to distinguish two different types of
to Shagrir (2010) the inner formal dependencies are formal
computational explanations. Firstly, there are interlevel
relations between inputs and outputs, and the outer formal
computational explanations, which explain by describing,
dependencies are mathematical relations between “what is
how the possible behavior or processes of a system is
being represented by the inputs and outputs”. These formal
governed by certain information processing principles,
dependencies are abstracted from representational contents,
rather than explain how certain algorithms compute certain
which correspond for example certain features of physical
functions. These computational explanations display the
environment.
function that the mechanism computes and they explain and
So, there are at least two different kinds of computational
why this function is appropriate for a given cognitive task.
explanations; the interlevel and the intralevel ones. In the
Some of our critics, such as Milkowski, have claimed that
following sections, we will argue that neither interlevel nor
we see these interlevel computational explanations as
intralevel computational explanations can be subsumed
“systemic explanations that show how a cognitive system
under the banner of standard mechanistic explanations. In
can have some capacities” (Milkowski 2013, p. 107).
the case of interlevel explanations, the problem is the
However, we do not defend such a position. We do not
direction of explanation (Rusanen & Lappi 2007), and in the
claim that computational explanations explain how a
case of intralevel explanations, the problem are the
cognitive system can have some capacities. Instead, what
dependencies that the explanations track (Rusanen 2014).
we claim is that interlevel computational explanations
Inter-level Computational Explanations: The
3
Although Marr´s notion of computational explanation is Problem of Direction
sometimes thought to be “outdated” and “oldfashioned”, it still In a nutshell, the problem for standard mechanistic accounts
plays an important role in cognitive and cognitive neurosciences. of interlevel explanations goes as follows: In standard
For example, there is interesting work being done in theoretical accounts (constitutive) mechanistic explanations are
neuroscience and cognitive modeling within this framework in the characterized in such a way that in inter-level computational
domains of vision, language, and the probabilistic approach to cog-
explanations, the explanans is at a lower level than the
nition (for overviews, see Anderson 1991; Chater 1996; Chater et
al. 2006). explanandum. For example Craver (2001, p. 70, emphasis
112
added) notes that “ (Constitutive) explanations are inward “mechanisms”, which are not causally or spatiotemporally
and downward looking, looking within the boundaries of X implemented.
to determine the lower level mechanisms by which it can Φ. In other words, the problem is that in standard
The explanandum… is the Φ-ing of an X, and the explanans mechanistic accounts, in contextual explanations the
is a description of the organized σ-ing (activities) of Ps (still “contexts” are expressed in causal and spatiotemporal terms,
lower level mechanisms).” not in terms of information processing at the level of
In those explanations, phenomena at a higher level of computational competences. Crucially, this kind of view
hierarchical mechanistic organization are explained by their conceives contextual explanations as a kind of systemic
lower-level constitutive causal mechanisms but not vice explanations, in which the uppermost level of the larger
versa (Craver 2001, 2006; Machamer & al, 2000). For mechanism will still remain non-computational in character.
example, under this interpretation a cognitive capacity For this reason, computational explanations are not these
would be explained by describing implementing “systemic” contextual explanations. In contrast, we claim,
mechanisms at algorithmic or implementing level. But, in computational explanations involve abstract mechanisms,
inter-level computational explanations, the competence which are not causally, but logically governing the behavior
explains performance i.e. explanans is at the level of of the mechanisms at the lower levels.
cognitive competences, and the explanandum is at the level
of performances. In other words, these inter-level Intra–level Computational Explanations: The
computational explanations proceed top-down, while Problem of Dependencies
constitutive mechanistic explanations are typically
Now, let´s move to the intralevel computational
characterized in such a way that they seem always to be
explanations. Why cannot they be seen as standard
bottom-up explanations. Thus, computational explanations
mechanistic explanations? Well, the answer is that they
are not constitutive mechanistic explanations in the standard
simply track different kinds of dependencies. While
sense.
algorithmic and implementation level explanation track
One might argue that this analysis ignores the possibility
causal or constitutive dependencies at the level of cognitive
that computational explanations are contextual rather than
or neural performances, intra-level computational
constitutive mechanistic explanations. In the mechanistic
explanations track formal dependencies between certain
terminology, the contextual explanations explain how the
kinds of information processing tasks at the level of
“higher-level” mechanism constrains what a lower level
cognitive competences.
mechanism does, and one computational mechanism can be
Because of this, these different modes of explanation are
a component of a larger computational system, while the
not necessarily logically dependent on each other. Thus the
latter serves as the contextual level for the former. For
computational explanations at the highest level may be
example Bechtel seems to accept this position, when he
formulated independently of assumptions about the
remarks that “since (marrian) computational explanations
algorithmic or neural mechanisms which perform the
address what mechanisms are doing they focus on
computation.
mechanisms “in context”” (Bechtel 2008, p. 26).
Some of our critics, such as Kaplan (2011) and Piccinini
Now, if computational explanations was contextual
(2009) remark that our position can be seen as a typical
explanations, then our argument would fail. Namely, if
example of “computational chauvinism”, according to
computational-level explanations were contextual
which computational explanations of human cognitive
explanations, and if contextual explanation is a subspecies
capacities can be constructed and confirmed independently
of standard mechanistic explanations, then computational
of details of their implementation in the brain.
level explanations would be a subspecies of mechanistic
Indeed, we defend the view that computational
explanations.
explanations can be in principle - if not in practice -
However, it is possible to argue that computational
constructed largely autonomously with respect to the
explanations are not contextual explanations in the standard
algorithmic or implementation levels below. That is:
mechanistic sense. For instance, Craver characterizes
computational problems of the highest level may be
contextual explanations as explanations, which “refer to
formulated independently of assumptions about the
components outside of X” and are “upward looking because
algorithmic or neural mechanisms which perform the
they contextualize X within a higher level mechanism”. On
computation (Marr 1982; see also Shapiro 1997; Shagrir
this view, a description of how a cognitive system
2001). Because the performance and competence- level
“behaves” in its environment, or how an organization of a
computational explanations track different kinds of
system constraints the behavior of its components, require a
dependencies, these different modes of explanation are not
spatiotemporal interpretation for the mechanisms. But, as
necessarily logically dependent on each other. Hence, if this
we argued in 2011, computational explanations do not
is computational chauvinism, then we are computational
necessarily refer to spatiotemporally implemented higher-
chauvinists.
level mechanisms, and they do not involve spatiotemporally
However, Kaplan (2011) claims that while we highlight
implemented components “outside of (spatiotemporally
the independence of computational explanations, we forget
implemented) X”. Instead, they refer to abstract
something important Marr himself emphasized. Namely,
113
Kaplan remarks that even if Marr emphasized that the same If computational explanations are characterized as
computation might be performed by any number of explanations which answer questions such as: “What is the
algorithms and implemented in any number of diverse goal of this computation?”, it may be claimed that we fail to
hardwares, Marr´s position changes when he “addresses the make a distinction between task analysis and genuine
key explanatory question of whether a given computational explanations.
model or algorithmic description is appropriate for the A task analysis breaks a capacity of a system into a set of
specific target system under investigation” (Kaplan 2011, sub-capacities and specifies how the sub-capacities are (or
p.343). may be) organized to yield the capacity to be explained.
Is this, really, an argument against our position? As Obviously, if computational explanations are mere
Kaplan himself remarks, Marr rejects “the idea that any descriptions of computational tasks, then they are not
computationally adequate algorithm (i.e., one that produces explanations at all.
the same input-output transformation or computes the same However, computational explanations are clearly more
function) is equally good as an explanation of how the than mere descriptions of computational tasks, because they
computation is performed in that particular system” (Kaplan describe formal dependencies between certain kinds of tasks
2011 p.343). and certain kinds of information processing requirements. If
But then, we are not talking about competence level these formal dependencies are such that descriptions of
explanations anymore. When the issue is how the them not only offer the ability to say how the computational
computation is performed in the particular system, such as layout of the system actually is, but also the ability to say
in human brains, then the explanation is given in terms of how it would be under a variety of circumstances or
algorithmic or neural processes, or mechanisms, if you will. interventions, they can be counted as explanatory4.
Then, naturally, the crucial issue is what kinds of In other words, if these descriptions answer questions
algorithms are possible for a certain kind of system, or such as “Why does this kind of task create this kind of
whether the system has structural components that can constraint rather than that kind of constraint?” by tracking
sustain the information processing that the computational such formal dependencies which can explain what makes
model posits at the neural level. If one aims to explain how the difference, then these descriptions can be explanatory.
our brains are able to perform some computations, then – of Obviously, computational explanations of this sort are not
course – one should take the actual neural implementation causal explanations. However, in the context of explanation
and the constraints of the possible neurocognitive of cognitive phenomena, it may be necessary to defend
architecture into account as well. more liberal and pluralistic views of explanation, which
But given this, these kinds of explanations are would allow that there are also some non-causal forms of
explanations at the algorithmic or performance level, not at explanation.
the computational or competence level. Because of this, we We agree with mechanists that when we are explaining
also find position defended by Piccinini & Craver (2011) how cognitive processing actually happens for example in
problematic. Piccinini and Craver (ibid) argue that in so far human brains, it is a matter of causal explanation to tell how
computational explanations do not describe how the the neuronal structures sustain or produce the information
computational system “actually works” i.e. describe “how processing in question. However, we still defend the view
the information is encoded and manipulated” in that there are other modes of explanation in cognitive
implementing system, they are mere how possibly- sciences as well.
explanations. In our understanding, this depends on the
explanatory questions. If, for example, the aim is to explain, Discussion: The Scope of Mechanistic
how certain kind of information processing task is actually Explanation
solved in human brains, and if the explanations does not
Some explanations of cognitive phenomena can be
describe how it actually happens, it is a how possibly-
subsumed under the banner of “mechanistic explanation”.
explanation. But, it is a how possibly explanation at the
Typically those explanations are neurocognitive
performance level, not at the competence level.
explanations of how certain neurocognitive mechanisms
For this reason, the remark that computational
produce or sustain certain cognitive phenomena, but also
explanations do not describe how the computational system
some psychological explanations can be seen as instances of
“actually works” is not an argument against the logical
mechanistic explanations. Moreover, if a more liberal
independence of the computational level explanations.
interpretation for the term mechanism is allowed, then some
computational or competence level explanations may also
The Explanatory Status of Computational qualify as mechanistic explanations (Rusanen & Lappi
Explanations 2007; Lappi & Rusanen 2011).
A more problematic issue is to what extent computational
explanations are explanatory after all. Although Milkowski
may partially misinterpret our position, he still raises an 4
important question concerning the explanatory character of This is a non-causal modification of the Woodward´s
manipulationist account of explanation (Woodward 2003). For a
computational explanations (Milkowski 2012, 2013). similar treatment of Woodward, see Weiskopf 2011.
114
Nevertheless, we think that there are compelling reasons explain many cognitive phenomena, such as certain forms of
to doubt whether mechanistic explanation can be extended linguistic patterns, or certain types of inductive
to cover all cognitive explanations. There are several generalizations, by combining these principles.
reasons for this plea for explanatory pluralism: Firstly, it is These explanations are “principle based” rather than
not clear whether all cognitive systems or cognitive mechanistic explanations. Moreover, Chater and colleagues
phenomena can be captured mechanistically. Mechanistic seem to suggest the mechanistic models of these phenomena
explanations require that the system can be decomposed i.e. may actually be derived from these general principles, and
analyzed into a set of possible component operations that explanations that appeal to these general principles provide
would be sufficient to produce or sustain the phenomenon in “deeper” explanations than the mechanistic explanations
question (Bechtel & Richardson 1993). Typically a (Chater & Brown 2008). It is possible, that many of the so
mechanism built in such a manner will work in a sequential called computational level explanations turn out to be
order, so that the contributions of each component can be instances of these principle-based explanations rather than
examined separately (Bechtel & Richardson 1993). instances of mechanistic explanations.
However, in cognitive sciences there are examples of In sum, taken together these diverse claims seem to imply
systems – such as certain neural nets – which are not that there is not a single, unified mode of explanation in
organized in such a manner. As Bechtel and colleagues cognitive sciences. Instead, they seem to suggest that
remark, the behavior of these kinds of systems cannot be cognitive sciences are examples of those sciences which
explained by decomposing the systems into subsystems, utilize several different modes of explanation, only some of
because the parts of the networks do not perform any which can be subsumed under the mechanistic account of
activities individually that could be characterized in terms of explanation.
what the whole network does (Bechtel & Richardson 1993; Obviously, mechanistic explanation is a powerful
Bechtel 2011, 2012). Hence, it is an open question to what framework for explaining the behavior of complex systems,
extent the behavior of these kinds of systems can be and it has demonstrated its usefulness in many scientific
explained mechanistically. At the very least, it will require domains. Also, many successful theories and explanations
adopting a framework of mechanistic explanation different in cognitive sciences are due to this mechanistic approach.
from the one that assumes sequential operation of However, this does not imply that it would be the only way
decomposable parts (Bechtel 2011, 2012; Bechtel & to explain complex cognitive phenomena.
Abrahamsen 2011).
Moreover, Von Eckardt and Poland (2004) raise the Concluding Remarks
question to what extent the mechanistic account is In this paper, we have argued that there are at least two
appropriate for those explanations which involve appeal to different kinds of computational explanations; the interlevel
mental representations or to the normative features of and the intralevel ones. Moreover, we have argued that
certain psychopathological phenomena. Although we find neither interlevel nor intralevel computational explanations
Von Eckardt and Poland´s argumentation slightly can be subsumed under the banner of standard mechanistic
misguided, we still think that it is important to consider the explanations. In the case of interlevel explanations, the
normative aspects of cognitive phenomena. Cognitive problem is the direction of explanation, and in the case of
systems are, after all, adaptive systems which have a intralevel explanations, the problem are the dependencies
tendency to seek “optimal”, “rational” or “best possible” that the explanations track.
solutions to the information processing problems that they Obviously, computational explanations of this sort are not
face. Because of this, cognitive processes are not only goal- causal explanations. However, in the context of explanation
directed, but also normative. It is not clear how well this of cognitive phenomena, it may be necessary to defend
normative aspect of cognitive systems can be captured by more liberal and pluralistic views of explanation, which
mechanistic explanations. would allow that there are also some non-causal forms of
Thirdly, some philosophers have paid attention to the fact explanation.
that there are examples of explanatory computational
models in cognitive sciences which focus on the flow of References
information through a system rather than the mechanisms
that underlie the information prosessing (Shagrir 2006,
2010). Along similar lines, Weiskopf (2011) argues that Anderson, J. 1991b. Is Human Cognition Adaptive?
there is a set of “functional” models of psychological Behavioral and Brain Sciences, 14: 471- 457.
capacities which are both explanatory and non-mechanistic. Bechtel, W. 2008. Mental mechanisms: Philosophical
Finally, in recent years cognitive scientists have raised the perspectives on cognitive neuroscience. London:
possibility that there are some universal, law-like principles Routledge University Press.
of cognition, such as the “principle of simplicity”, Chater, N. 1996. Reconciling Simplicity and Likelihood
“universal law of generalization” or the “principle of scale- Principles in Perceptual Organization. Psychological
variance” (Chater & al 2006; Chater & Vitanyi 2003). Review, 103(3): 566-581.
Chater and colleagues (ibid.) argue that it is possible to
115
Chater, N., & Vitanyi, P. M. B. 2003. The generalized Shagrir, O. 2010. Brains as Analog-Model Computers.
universal law of generalization. Journal of Mathematical Studies in the History and Philosophy of Science, 41(3):
Psychology, 47: 346-369. 271-279.
Chater, N., Tenenbaum, J. B., & Yuille, A. 2006. Shapiro, L. 1997. A Clearer Vision. Philosophy of Science,
Probabilistic Models of Cognition: Conceptual 64, 131-153.
Foundations. Trends in Cognitive Sciences, 10, 287-291. Weiskopf, D. 2011. Models and mechanisms in
Chater, N. & Brown, G. From Universal Laws of Cognition psychological explanation, Synthese, 183: 313-38.
to Specific Cognitive Models. Cognitive Science, 32, 36- Woodward, J. 2003. Making Things Happen: A Theory of
67. Causal Explanation. Oxford: Oxford University Press.
Craver, C.F. 2001. Role functions, Mechanisms and
Hierarchy. Philosophy of Science, 68, 53-74.
Craver, C.F. 2006. When Mechanistic Models Explain.
Synthese, 153: 355-376.
Kaplan, D. 2011. Explanation and description in
computational neuroscience. Synthese, 183 (3): 339-373
Lappi, O. & Rusanen, A-M. 2011. Turing Machines and
Causal Mechanisms in Cognitive Sciences, In P. McKay
Illari, F. Russo & J. Williamson, (eds.) Causality in the
Sciences. Oxford: Oxford University Press. 2011: 224-
239
Machamer, P. K., Darden, L., & Craver, C. 2000. Thinking
About Mechanisms. Philosophy of Science, 67: 1-25.
Marr, D. 1982. Vision: A Computational Investigation into
the Human Representation of Visual Information. San
Francisco: W.H. Freeman.
Milkowski, M. 2012. Limits of Computational Explanation
of Cognition. In Müller, V. (ed.) Philosophy and Theory
of Artificial Intelligence. Springer.
Milkowski, M. 2013.Explaining the Computational Mind.
MIT Press.
Piccinini, G. 2004a. Functionalism, Computationalism and
Mental Contents. Canadian Journal of Philosophy, 34,
375-410.
Piccinini, G. 2006a. Computational Explanation and
Mechanistic Explanation of Mind. In M. DeCaro, F.
Ferretti & M. Marraffa (Eds.), Cartographies of the Mind:
The Interface Between Philosophy and Cognitive Science.
Dordrecht: Kluwer.
Piccinini, G. 2006b. Computational Explanation in
Neuroscience. Synthese, 153, 343-353.
Piccinini, G. & Craver, C. 2011. Integrating psychology and
neuroscience: functional analyses as mechanism sketches.
Synthese, 183 (3):283-311.
Piccinini, G. 2011. Computationalism, in Oxford Handbook
of Philosophy of Cognitive Science, Eric Margolis,
Richard Samuels, and Stephen Stich, eds., Oxford:
Oxford University Press 2011: 222-249.
Rusanen, A-M. & Lappi, O. (2007). The Limits of
Mechanistic Explanation in Neurocognitive Sciences. In
Vosniadou, S., Kayser, D. & A. Protopapas, (Eds)
Proceedings of the European Cognitive Science
Conference 2007. Howe: Lawrence Erlbaum Associates.
2007: 284-289.
Newell, A., & Simon, H. A. (1972). Human problem
solving. Englewood Cliffs, NJ: Prentice-Hall.
116