∗ΜΡΕΠ ΗςΕϑΞ
Logic and Cognition: Two Faces of Psychologism
Mariusz Urbański
Abstract
In this paper two concepts of psychologism in logic are outlined:
the one which Frege and Husserl fought against and the new psychologism, or cognitivism, which underlies a cognitive turn in contemporary
logic. Four issues such cognitively oriented logic should be interested
in are indicated. They concern: new fields opened for logical analysis, new methods and tools needed to address these fields, neural basis
of logical reasoning, and an educational problem: how to teach such
logic? Several challenging questions, which arise in the context of these
issues, are listed.
Keywords: Logic, reasoning, new psychologism, cognitivism.
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Introduction
Logic emerged in Antiquity as an investigation of types of reasoning, both
from the perspective of case-based analysis of their rationality, and from
the perspective of their structures. So conceived, for many centuries logic
stood in a close and natural relationship to the science of actual reasoning
processes. As long as both logic and psychology were just parts of philosophy there was no real need for any precise demarcation. Boole [1854, p.
1] searched for “the fundamental laws of those operations of the mind by
which reasoning is performed [and] some probable intimations concerning
the nature and constitution of the human mind”. For Mill [1858, p. 7] logic
was the science of “both the processes itself of proceeding from known truths
to unknown, and all intellectual operations auxiliary to this”. For de Morgan [1847, p. 26] it was “the branch of inquiry [...] in which the act of the
mind in reasoning is considered”. Beneke [1832, p. 12] classified logic as
the part of psychology that investigates relations between thinking and the
reality. Thus when Erdmann [1870, vol. 3] coined the term ‘psychologism’
to describe Beneke’s views it was merely a neutral description.
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Psychologism: the repulsive face vs. the alluring one
Logic and cognition got ‘divorced’ (as Stenning and van Lambalgen [2008,
p. 8–15] call it) mainly because of the antipsychologistic argumentation of
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Gottlob Frege1 and his proselyte Edmund Husserl. From the perspective of
logic treated as a formal system, in the spirit of Fregean Begriffsschrift, the
only interesting properties of actual reasoning are the objective ones: their
structure, the relations between premises and a conclusion (propositions
rather than sentences). Laws of logic are known a priori, they are not
generalizations of experiences. Laws of logic refer to ideal objects, not to
psychological entities. Actual thinking is not driven by the laws of logic
[Husserl, 1900–1901, §§ 19–23]. Logic (and mathematics) is the most exact
of all sciences, while psychology is imprecise and vague [Frege, 1884, p. 38].
The one has nothing to do with the other. After Frege and Husserl in formal
logic the term ‘psychologism’ began to be associated negatively.
Achievements of this logic – call it formal, mathematical or symbolic –
are enormous, especially when compared with a rather stable development of
so-called traditional logic (from Aristotle to de Morgan). But the antimetaphysical enchantment by the Pure Form, so typical for Frege’s pugnacious
grandchildren (logical empiricists in particular) soon had to give place to
a more realistic stance. Restoring the good name of the Truth by Tarski,
Gödel’s theorems, developments within philosophical logic and logical pragmatics are only a few steps towards inclusion into contemporary logic’s area
of interest, the problems of representation of structures of thought and language, that “go beyond the bare minimum provided by standard first-order
logic” [van Benthem, 2008, p. 71]. It is important that the source of all this
changes was reflection on a real thought and on a real language even if sometimes this source has been viewed as a bit embarrassing. The farther steps
are marked by mutual infiltration of logic and Artificial Intelligence, in particular with respect to problem-solving, planning and diagnosis [Charniak
and McDermott, 1985], and by granting a logical citizenship to an analysis
of informational and heuristic value of fallacies [Van Eemeren et al., 1996].
Nowadays we are witnessing a ‘practical’, or cognitive, turn in logic
[Gabbay and Woods, 2005]. It does not declare results by Peano, Frege,
Skolem or Tarski null and void. It claims that logic has much to say about
actual reasoning and argumentation. Moreover, high standards of logical
inquiry that we owe to Peano, Frege, Skolem, Tarski and others offer a new
quality in research on reasoning and argumentation. Having in mind Corcoran’s [1994] distinction of logic as formal ontology and logic as formal
epistemology we may say that the aim of the practical turn is to make such
formal epistemology even more epistemically oriented. This is not to say
that this ‘practically turned’ (or cognitively oriented) logic becomes just a
part of psychology. This is to say that this logic aquires a new task of “systematically keeping track of changing representations of information” [van
Benthem, 2008, p. 73] and that it contests the claim that distinction be1
Frege’s work is the finial of the ‘mathematical turn’ in logic that was initiated by
Leibniz [Gabbay and Woods, 2001].
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tween descriptive and normative account on analysis of reasoning is disjoint
and exhaustive [Gabbay and Woods, 2003, s. 37]. From different than a
purely psychological perspective logic becomes – again – interested in answering Dewey’s question: how we think? This is the new alluring face of
psychologism (or cognitivism, as I prefer to call it) in logic, as opposed to
the repulsive one, which Frege and Husserl fought against.
In my opinion there are at least four issues this cognitively oriented
logic should be interested in. They are not of the same interest for every
logician; nevertheless, all four are important if the renewed logical interest
in actual human reasoning is to be considered as a serious one. These four
issues concern: new fields opened for logical analysis, new methods and
tools needed to address these fields, neural basis of logical reasoning, and,
last but not least, an educational problem: how to teach such logic? All
of them confront logic with exciting challenges and I am going to list some
questions which arise in their context. Let us have a closer look at the four
issues.
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3.1
The four issues
New field
Most important proponents of the practical turn in logic emphasize that
‘practicality’ means first and foremost application of logic to the analysis of
actual human reasoning:
Logic is of course not experimental, or even theoretical, psychology, and it approaches human reasoning with purposes of its
own. And a logical theory is not useless if people do not quite
behave according to it. But the boundary is delicate. And I
think the following should be obvious: if logical theory were
totally disjoint from actual reasoning, it would be no use at all,
for whatever purpose! [van Benthem, 2008, p. 69].
Two main problems arise in this context. First is the problem of application: what real (reasoning) cognitive processes, if any, are modelled by a
given logical system? It is not the case that, if the answer is ‘hard to say’,
the system in question is worthless. But it is more interesting from the cognitive point of view when such an aswer can be determined. However, one
warning is in order here. It is well-known that the number of logical systems
exceeds the number of stars in the sky (every modal logician will agree). It is
probably pointless to try a jacket of every single system on a body of human
cognition just to conclude ‘it does not fit!’. If we are interested in question
on what kind of logics real human reasoning is based, the second problem
should be considered. This is the problem of extraction: Is it possible to
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extract underlying logics from our cognitive processes? Again, it would be
rather pointless to attempt at such extraction from scratch: the problems
of application and of extraction are interwined. Two short examples should
clear the matter.
First example comes from a paper by Strannegård et al. [2010]. The
authors conducted an experiment in which a random mix of 40 tautologies
and 40 non-tautologies were presented to the participants, who were asked
to determine which ones of the formulas were tautologies, with 45 s timelimit. On the basis of the results the authors propose a proof formalism for
modelling propositional reasoning with bounded cognitive resources. They
also define two particular proof systems for showing propositional formulas
to be tautologies or non-tautologies.
What is really interesting is that the authors aimed at modelling real (or,
to be more precise: as real as possible) reasoning processes, incorporating
fundamental concepts and findings from cognitive psychology, concerning
memory and reasoning processes, into their natural deduction style proofs.
The resulting proof systems are expressed in an augmented language of Classical Propositional Calculus, extended to reflect reasoning processes involved
in deciding if a given formula is a tautology or not (this is a kind of a ‘language of thought’ in the sense of Stenning and van Lambalgen [2008]). Rules
of their systems aim at capturing, among others, observations of logical form
of a formula, partial truth-functional evaluation of a formula, trading information for working memory space. Of particular interest is the following
quotation from “Development Process” section of the paper:
Our proof systems were developed on the basis of existing proof
systems and cognitive models, interviews with the participants,
think-aloud protocols, introspection, and experimental data
[Strannegård et al., 2010, p. 300].
It is an open question whether this particular formalism is (cognitively)
adequate. Nevertheless, it is clear that in process of such a development
both application and extraction are interwined, providing feedback to each
other.
The second example is even more instructive as it reveals how productive
is transcending one-dimensional interpretations of experimental results on
human reasoning. It is the problem of interpretation of Wason’s selection
task, as described by Stenning and van Lambalgen [2008, ch. 3]. In this
well-known task a subject is presented with a set of four cards, labelled with
letters and numbers (one typical set of labels is ‘A’, ‘K’, ‘4’, ‘7’). The subject
can see only the exposed face of cards and not the hidden back. On each
card, there is a number on one of its sides and a letter on the other. The
following rule is also presented to the subject:
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If (p) there is a vowel on one side, then (q) there is an even
number on the other side.
The subject is informed that the rule applies only to the four cards and
that the task is to decide which, if any, of these four cards must be turned in
order to decide if the rule is true. The subject should not turn unnecessary
cards.
If the conditional rule is interpreted as a material implication, then the
correct solution of the task consist in applying modus ponens and modus
tollens and the card that should be turned are the ones labelled with ‘A’
and ‘7’. The abstract, context-independent version of the task (as described
above) yields typically 5% – 20% of correct answers. The results are almost
reversed if the rule is construed in such a way that it concerns practical
matters (like the rule ‘if you drink alcohol here, you have to be over 18’ in
research conducted by Griggs and Cox [1982]).
But dialogue protocols quoted by the authors reveal that there is a number of pragmatic factors that affect solution of selection task in the abstract
setting. Among them are: subject’s understanding of truth and falsity of
conditionals, descriptive vs. deontic interpretation of conditional, considering conditional as a rule which allows exceptions. In their fascinating
analysis Stenning and van Lambalgen show that it is a misunderstanding
just to claim that classically incorrect solutions to the selection task are
simply irrational. They argue that:
understanding [subject’s] interpretation sometimes leads to clarification of what subjects are trying to do, and that often turns
out to be quite different than the experimenter assumes [Stenning and van Lambalgen, 2008, p. 90].
The experimental data support the claim that humans are quite fluent
‘practical logicians’ [Riggs and Peterson, 2000; Scribner, 1997]. Much like
a proficient tennis player, who is able to catch a difficult service ball and
send it back to his opponent without much knowledge of geometry, we are
able to apply different logics properly in different everyday contexts. We
are capable of performing simple deductive inferences if needed, we can
do reasonable abductions, even we are able to reason non-monotonically
under the closed-world assumption. Of course, it is human to err in playing
tennis as well as in reasoning. But still, several questions arise: If there are
many different logics involved in our everyday reasoning processes, and if
they are applicable in different tasks, and if we can switch smoothly between
them, then maybe there exists a cognitive (meta)mechanism managing their
applications? A mechanism for deciding, for example, which criteria for
evaluating conclusions should be applied in a particular case? And maybe
such mechanism can be formally modelled?
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3.2
New methods and tools
One problem with applying logic to actual human reasoning is, that this
reasoning often consists of non-verbal representations as premises and conclusion (consider geometrical proof without words [Nelsen, 1997] or different
kinds of non-verbal abduction [Magnani, 2009]). Another problem is, that
even more often reasoning rests on factors that are beyond reach of typical
logical formalisms (like ordering premises in certain reasoning according to
some pragmatic criteria of preference). Thus, as a result of expanding its
area of interest, cognitively oriented logic faces the need of extending both
the repertoire of its methods and the set of its tools.
An attractive direction of such an extension is connectionism. It is not
because artificial neural networks (ANNs) are adequate models of human
brain activity (they are not, as yet). What is really enticing is that ANNs
allow for modelling phenomena which escape symbolic languages.
A good example is the role of emotions in abductive reasoning. Thagard [2006, 2007] argues that every serious theory of abduction must take
emotional context of this kind of reasoning into account. On the one hand,
abduction is triggered by emotions: we start abducing when we encounter
surprising phenomena that are worth to be accounted for (and Magnani
[2009] argues that ‘we’ has a broader meaning than ‘we, humans’). On the
other hand, abductive finale is also of emotional character: if we manage
to make sense of puzzling facts the result is satisfaction (consider typical
endings of Holmesian detective stories, great examples of employing abduction in solving mysteries). There are some prospects concerning modelling
emotions via symbolic logic [Adam et al., 2009]. Nevertheless, models employing ANNs look more convincing [Eliasmith, Thagard, 2001; Thagard,
Litt, 2008]. Connectionist logics already open a new dimension in proof theory [d’Avila Garcez et al., 2008], but this novelty is of quantitative character,
similar to the one offered by a new proof technique. An open and interesting
question is if connectionist logics may offer also qualitative novelty, resulting
in something comparable to intensional revolution in logic.
Another attractive direction of extension of methods and tools of logic
is application of Labelled Deductive Systems [Gabbay, 1996]. Although the
idea of using labels in logic is not new, Gabbay is right in stressing that it
is new to consider the labelling as part of the logic [Gabbay, 1996, p. 12,
footnote 5]. Again, abduction is a good example. One step in such a reasoning consists in evaluation of generated hypotheses against certain predefined
criteria. In a realistic stance this means more than just checking consistency
or logical dependencies between hypotheses and background theories. There
are some pragmatic criteria that have to be taken into account, like Peircean
economy, testability or explanatory power. In the setting of Labelled Deductive Systems such criteria and evaluation of hypotheses against them may
be embedded directly into inference mechanisms, this time of a symbolic
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character.
3.3
Neural basis
Third issue for cognitively oriented logic is the neural basis of logical reasoning. It is not just a neuroimaging problem of what parts of the brain are
responsible for performing such operations. This question is probably of
interest, but not that much for logicians. Much more interesting question is
if logical reasoning is performed by the same parts of the brain that other
kinds of reasoning? In an fMRI study Monti et al. [2009] compared logical
inferences relying on sentential connectives (like: not, or, if . . . then) to linguistic inferences based on syntactic transformation of sentences involving
ditransitive verbs (like: give, say, take). The results indicate that logical inference is not embedded in natural language. Thus further questions arise:
What about logical vs. mathematical reasoning? And what about different
logics? Are regions of the brain recruited in epistemic or deontic inferences
the same as in ‘classical’ sentential inferences? Are erotetic inferences (that
is, inferences involving questions) processed by the same regions that declarative ones? And what about non-verbal logical inferences?
3.4
Educational concern
A fundamental educational problem is that to make sense of the interplay
of logic and psychology one needs a substantial competence in logic. For a
student this means going trough the foundations of set theory, model theory,
classical and some non-classical systems and their metatheory before he or
she will be able to grasp the idea of even the basic applications of logical
analysis to reasoning processes. And this way may be seen as quite a trying
one. Thus, in teaching logic, how to avoid Scylla of trivial narrative without proper formal basis and Charybdis of excessively hermetic formalism?
How not to reduce logic neither to critical thinking exercises, nor to formal
mindteasers, a kind of mind fitness for our students? How to teach logic
as both formally and empirically grounded science of reasoning processes?
How to design a cognitively oriented course in logic, which is a subject of
secondary importance in a typical curriculum? This is probably the most
practical and challenging problem of all I mentioned in this paper.
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Closing remarks
The practical turn does not create a rival for the mathematical logic. It
forms a next step in the development of logic which results in inclusion of
some areas of cognitive science, psychology and computer science into its
hard core. Consequently, logic becomes capable of modelling actual cognitive activity of real life agents. Thus, as Gabbay and Woods [2001, s.
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141] put it, “whereas mathematical logic must eschew psychologism, the
new [that is, cognitively oriented] logic cannot do without it”: this new psychologism, or cognitivism, constitutes the essence of logic so conceived. A
paraphrase of Einstein’s famous formulation may serve as its catchword: in
analysis of reasoning psychology without logic is lame, whereas logic whitout
psychology is blind.
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Mariusz Urbański
Chair of Logic and Cognitive Science
Institute of Psychology
Adam Mickiewicz University
Poznań, Poland
Mariusz.Urbanski@amu.edu.pl
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