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Why and How Diagrams Help in Teaching Syllogistic 

Skills: An Embodied Account 
 

Menno van Calcar 

 
 

Abstract: Teaching syllogistic reasoning is often perceived as teaching pupils the purely 
formal rules of deductive inference. According to this common conception, such reasoning 
is a highly abstract skill, one that is carried out by the processing of syntactically encoded 
representations of the premises. This paper argues that syllogistic reasoning may, indeed, 
keep clear of the concrete contents of the premises, but is realized by a skill that is less abstract 
than rule-following. It argues that reasoning is continuous with our other skills and is realized 
by our capacities to deal with spatial situations. This explains why the use of Venn diagrams, 
a much-used technique for evaluating syllogistic inferences, is effective: the spatial layout 
expressed by the diagrams directly activates the actual mechanism reasoners use. Teachers 
are therefore right when they teach the use of such diagrams. This paper also argues that 
using tools that tap into our capacities to deal with a three-dimensional world will be even 
more effective and corroborates this argument with an experiment in which three-
dimensional Venn diagrams were used to train high school pupils.  
Keywords: syllogisms, spatial capacities, three-dimensional Venn diagrams, embodied 
cognition 

 

Introduction 

 
 

t is not contested that teaching should foster critical thinking skills, on any level of 
education. One of the most important ones of these is the skill to reason. In a world rife 
with complex situations, and bad and deceptive reasoning, the skill to distinguish between 

valid and invalid inferences is essential for problem solving and decision making. Since Frege, 
many powerful formal logical systems have been developed. But most of us, and most of our 
pupils, don’t encounter, or use, reasoning in formal guise. In real life, we mostly encounter 
reasoning in written or spoken assertions, and the relations that are supposed to hold between 
those assertions (Johnson, 1996). In addition, formal logical systems are often quite inaccessible, 
unattractive to the not-mathematically-inclined, and counter-intuitive (Larvor, 2004). Informal 
logic, on the other hand, is about statements and inferences in natural language. This makes it 
recognizably relevant as something that plays a role in all domains of human life, makes it 
accessible to most pupils, and makes it suitable for many different didactical approaches. That’s 
why informal logic should be the basis of teaching reasoning skills.1 
 

 
1 Many even equate informal logic with critical thinking itself, e.g., Siegel, 2007. 

I  



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Syllogistic reasoning (e.g. all men are mortal, Socrates is a man, therefore Socrates is mortal) 
is at the core of informal logic, works with everyday sentences, and its basics can be easily grasped. 
In other words: teaching syllogistic reasoning is very suitable for fostering critical thinking skills. 
Working with syllogisms specifically trains the ability to tell valid (does the conclusion really 
follow?) from invalid arguments, enhancing the ability to be critical of reasoning, including one’s 
own.  

 
But how does one evaluate validity in syllogisms? If I try and catch my own preferred 

strategy, I find that I almost invariably express the meaning of the premises in Venn diagrams, 
spatially representing the given sets as circles that are distinct, overlapping, include each other, 
etc. For example, I understand the classic syllogism about the mortality of Socrates, that I just 
mentioned, as a spatially expressed set (circle) of ‘mortal entities,’ containing a spatially expressed 
set of ‘men,’ with Socrates being one specimen of the latter set, and therefore as one specimen of 
the former set. 

 
 

 

 

  

     

 

 

 

 
This is, of course, only the impression I get from personal experience, and anyone claiming 

that introspection revealed something else to them is just as right as I am. Still, the phenomenon 
of ‘circling,’ as I will call the use of Venn diagrams, whether in actual drawing or in ‘the mind’s 
eye,’ seems to be widespread (Ford, 1995; Bacon, Handley, and Newstead, 2003; Khemlani, 
2021). Reflecting on the premises and reflecting on necessitated conclusions without calling forth 
some version of circling seems to be the exception (Johnson-Laird, 2001). Furthermore, using 
such diagrams enhances subjects’ performance in syllogistic reasoning (Sato and Mineshima, 
2015).  

 
This is remarkable from the point of view of cognitive science’s dominant paradigm of 

cognitivism. Cognitivism claims that all cognitive performance is the result of the internal 
processing of symbolic entities called ‘representations’ (Thagard, 2018), and physically drawing 
spatial shapes such as diagrams surely isn’t internal, and internal representations of such shapes 
don’t seem to be purely symbolic (remember that symbols are only conventionally connected to 
what they’re supposed to be about, and spatial shapes seem to be, well, spatial). Cognitivism’s 
account of reasoning steers educators toward an approach in which the abstract rules of symbol 
processing are key, and away from drawing, moving, visualizing, etc. In this view, approaches to 
teaching logic that uses the body, movement, or artefacts, are misdirected. 

 
But the phenomenon of circling raises doubts about such an account: how can using circles 

enhance reasoning skills? Either cognitivism has to grant the act of drawing to be part of the 
cognitive processing, or cognitivism will have to grant that internal, but not symbolic, 

Mortal 

Men 

X Socrates 



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representations are part of the cognitive toolkit. If the first option is chosen, cognitivism yields 
to a version of extended, or even enactive, cognition theory. If the second option is chosen, 
cognitivism accepts that -some- internal representations are not disconnected from the rest of the 
body, world, or action. Such representations must then be conceived as somehow shaped by our 
embodiment, meaning that the fact that we are creatures who experience life in a three-
dimensional world has a profound influence on how we process syllogisms. 

 
In this paper, I argue that our skill in syllogistic reasoning is based on a skill we are much 

more familiar with, namely, our skill in engaging with the spatial aspects of our lives. Our 
acquaintance with spatial relations, afforded by our body and our ability to move through a three-
dimensional world, lies at the core of what seems to be a completely disembodied intellectual act. 
We circle, because we primarily (pre-reflectively) grasp syllogistic relations as spatial relations. It 
is only after reflection that we derive formal rules. Therefore, I argue that we should prefer an 
embodied account of syllogistic reasoning (Van Calcar, 2023a, Van Calcar, 2023b).2 The 
embodied account also explains why using Venn diagrams as a pedagogical tool works, as many 
teachers know, and that using drawing, motion, visualization, etc. in teaching is not misdirected. 

 
This paper first sketches cognitivism’s account of syllogistic reasoning and the role of Venn 

diagrams. In Section 2 some reasons to distrust cognitivism and prefer an embodied account of 
syllogistic reasoning are offered. Sections 1 and 2 are quite technical, arguing for an embodied 
understanding of syllogistic reasoning. If the reader is primarily interested in the method I 
designed to teach this skill, they might skip these. In Section 3, I present an experiment I 
conducted to substantiate the paper’s hypothesis. In Section 4, I give some pointers for using 
Section 3’s setup as a teaching tool. Finally, I offer a short summary and discussion. 
 

1. Cognitivist Accounts of Circling 
 

Venn diagrams have been extensively studied and have intricate relations with fundamental 
issues in logic. However, Venn diagrams are, even to John Venn himself, primarily a pedagogical 
device (Verburgt, 2023), so we do not have to delve into the technical subtleties connected to 
logical analysis. With Venn diagrams, one expresses the premises as related sets and evaluates 
whether a stated conclusion is valid. At this point, it might be worthwhile to remember that 
validity is different from truth: to evaluate validity, we ignore the truth value of the premises, and 
focus on the relations between them. For instance, we should ignore the truth value of the 
premises of: 
 
[1] 1. No human is a mammal, 
 2. All humans are mortal. 

 
Therefore, 
 

 3. Some mammals are mortal. 

 
2 Van Calcar, M. “A Plea for Wild Philosophy: how thinking about online philosophy teaching shows that doing 
philosophy well is like being an elephant in the jungle.” Teaching Philosophy, 46, 3 (2023a); Teaching Philosophy with 
LEGO.” Metodo 11 (2023b). 



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and just look at their possible relation(s). 1. and 2. can be spatially expressed as in which A, B, 
 

 

 

 

 

[1’]  

Humans          Mammals 

             A          B         C 

 

 

 

 

 
and C are the several possibilities afforded by premise 2. Conclusion 3. leaves out possibility A, 
in which premise 1. is satisfied (humans and mortals do not overlap, expressing that no human 
is a mammal), and premise 1. is also satisfied (all humans are contained by circle A, being mortal). 
However, no mammal is contained by A, suggesting the possibility that no mammal is mortal. 
That means that the conclusion is not necessitated by the premises, making the argument invalid, 
even if the conclusion is true. 
 

So how would a cognitivist analyze the role of such diagrams in syllogistic reasoning? 
According to cognitivism, anything outside of the central nervous system can only be a source of 
input and arena for output. Using diagrams then is a kind of epistemic action, whereby one 
manipulates the world in such a way as to reduce cognitive load (called ‘cognitive offloading’).3 
In other words, diagrams are tools that alleviate the task at hand, by stabilizing information 
(mental ‘grasping’ of propositions is prone to shifts and errors), relieving the load on working 
memory, and thereby creating cognitive capacity for further -internal- processing. One can 
compare this to writing down a grocery list, or to a professional barkeeper that uses different 
glasses to remember the order he just got (Beach, 1993). The Venn diagrams are used as follows: 
the reasoner reads (or hears) the premises, encodes their content (information) into 
representations, processes these representations, and decodes the result of that processing in 
afferent signals that lead to the motor activity of drawing diagrams. The diagrams are, thus seen, 
expressions of internal cognitive processes, on a par with other motor activity. The drawings can 
then serve as available input, to be encoded, processed, etc. In other words, if all went well, the 
Venn diagrams are just translations of the premises and their interrelation in a new format. That 
such drawing enhances syllogistic skill is presumably an effect of the way the information is 
presented in this new format, being processed into a helpful, ‘easier-to-digest’, form (Bauer and 
Johnson-Laird, 1993; Tversky, 2001; Giardino, 2015; Jamnik, 2021).4 It seems obvious how one 

 
3 This is explained in Cognitive Load Theory, a highly influential theory in the psychology of learning and education 
(Sweller, Ayres, and Kalyuga, 2011). The term ‘epistemic action’ was coined by Kirsh and Maglio (1994). It denotes 
a kind of action that alters the outside world in order to ease a cognitive (epistemic in their case) task. 
4 Encoding information into smaller units is called chunking. A reasoner might encode information into a different, 
‘lighter’, format. One might, for instance, encode a string of numbers like 033120248 into birthdate (March 31st), 
current year (2024), and current age of oldest child (8). Thereby the reasoner relays part of the processing to long-



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gets better at this; neuronal changes make for faster and more accurate processing, observable in 
faster and more accurate drawing of diagrams, and faster and more accurate further production 
or evaluation of syllogistic conclusions. 

 
So, what happens when one doesn’t draw, but somehow internally represents such 

diagrams? People who have had experience with drawing diagrams are known to visualize 
diagrams when tackling syllogisms, and, when skilled at this, to outperform those who don’t (Sato 
and Mineshima, 2015). In trained reasoners, pen and paper seem to become redundant. A 
cognitivist assumes that the representation is an encoded symbolic version of the content of the 
premises. In that way it is not different in kind from the mental representations of any part of 
the world, factual or hypothetical. The visualized diagrams can, as representations, become part 
of cognitive processes, in the same way any representation can. Therefore, internal diagrams work 
-almost- as well as drawn diagrams. The experience taken from external drawing has caused neural 
changes, and those neural pathways make it possible for a reasoner to do without the external 
props. 

 
However, if we allow diagrammatic representations to be part of proper cognitive 

processing, they cannot reduce cognitive load. Being mental representations, they do not stabilize 
information, or free up working capacity, because they are part of the processing itself. Adding 
such representations to the processing might even add to the workload, because they would be 
just more representations to process. This is a serious problem for cognitivism, because, without 
a solid argument on why using mental diagrams makes processing faster and more accurate, 
cognitivists haven’t really explained anything. Stating that such use simply does enhance 
efficiency, is just another way of assuming the conclusion. The question is how and why an internal 
diagrammatic representation helps in deducing. 

 
In the next section we will argue that this question cannot satisfactorily be answered by 

cognitivism, and that we should look at an embodied explanation. 
 

2. Embodied Accounts of Circling 
 

Cognitivism gets challenged by a family of theories, often referred to as theories on 4E-
cognition (with the E’s standing for embedded, extended, embodied, and enactive), that claims 
that we cannot satisfactorily explain cognition without taking the environment, body, and action 
into account. It basically argues that only studying the brain to understand cognition is like only 
studying the boat’s rudder to understand sailing. One of the most compelling arguments to 
distrust cognitivism comes from evolutionary considerations: humans have developed to 
efficiently deal with challenges, relying for a big part on their cognitive capacities. That means 
that human cognition is bound to be realized by bodily interactions with the world, making 
cognitivism’s insistence on the brain’s isolated processes quite idiosyncratic. It seems much more 
likely that the brain’s activity is not some anomalous processing of detached symbols, but 
continuous with (processes in) the real world. 

 
term memory, reducing the load on short-term memory. However, it is far from clear how encoding information 
into spatial arrays is a form of chunking. Moreover, it does not explain why chunking would use spatial arrangements. 



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The E-family has had considerable success in giving descriptions and explanations of so-

called lower order cognition. Instances of catching balls, finding the way to a museum, and using 
your fingers to count, can be accounted for without, or with a minimal role for, symbolic 
representations (McBeath et al., 1995; Clark and Chalmers, 1998; Dehaene et al., 1999). 
However, higher order cognitive phenomena, such as imagining, planning, and reasoning, are 
harder to constitutively connect to embodied action. Such phenomena seem, at first glance, to 
be thoroughly disconnected, and seem to exclusively take place in some internal realm of the 
mind. However, there is, at second glance, a constitutive (and thus not merely supportive) role 
for embodiment in syllogistic reasoning. 

  
One of the members of the 4E-family is Grounded Cognition Theory. This theory argues that 

the stuff that realizes cognition, concepts, and thus the words we think with,5 is rooted in 
sensorimotor experience. It thus argues against cognitivism’s idea that representations are 
symbolic, detached from physical reality, or amodal:  

 
The core knowledge representations in cognition are not amodal data structures that exist 
independently of the brain’s modal systems. Instead, according to a positive definition of 
grounded cognition—the environment, situations, the body, and simulations in the brain’s 
modal systems ground the central representations in cognition. From this perspective, the 
cognitive system utilizes the environment and the body as external informational structures 
that complement internal representations. In turn, internal representations have a situated 
character, implemented via simulations in the brain’s modal systems, making them well 
suited for interfacing with external structures. (Barsalou, 2010: 717) 
 

A plethora of research has demonstrated this claim for concrete words, like action verbs 
and concrete nouns. Behavioral data, neuroimaging, somatotopic relations, corpus studies, 
Transcranial Magnetic Stimulation, etc., have shown that such words are inextricably bound to 
embodied experiences, and with embodied (re)actions (overviews in Barsalou, 2008; 2020; Pecher 
and Zwaan, 2010). On reading ‘kick’, for instance, cortices dedicated to the motoric act of kicking 
get activated (Hauk et al., 2004). The idea is that words associated with experienced action, or 
other sensorimotor experiences, reactivate the neural structures that were activated during the 
actual experience. The neural circuitry engages into a simulation of the experience. 

  
Grounded Cognition approaches, like Conceptual Metaphor Theory (CMT), are even able to 

construe abstract concepts, like JUSTICE, as -at least partly- embodied. CMT argues that such 
concepts are based on concrete concepts through metaphor. We understand concepts of things 
that we haven’t had any experience with, by mapping those onto the things we are familiar with, 
because we have had sensorimotor experience with the latter (Lakoff and Johnson, 1999; Lakoff 
and Nuñez, 2001). When we think about time, for instance, we use concepts about space. Time 
goes by, the future is forward, things happen after or before other events, etc. (Nuñez, 1999). By 
mapping TIME onto SPACE, we gain understanding of TIME through our acquaintance with 
SPACE. CMT demonstrates that we recruit so-called image schemas, concepts that are mostly 

 
5 Like most things worth thinking about in philosophy, the relation between words and concepts is debated. Let’s 
forego this debate and accept the widely held conviction that words and concepts are intimately connected. 



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about spatial relations and movements, to deal with challenges that are not about space or 
movement. Image schemas function as structuring systems for other concepts (Grady, 1997). For 
instance, the image schema of CONTAINER enables thinking about people being IN a team, 
things being OUT of sight, and falling IN love. As Lakoff and Johnson write in their seminal 
Metaphors We Live By: 
 

[W]e typically conceptualize the nonphysical in terms of the physical – that is, we conceptualize 
the less clearly delineated in terms of the more clearly delineated. (Lakoff and Johnson, 2003: 
59) 
 

The structure of the ‘more clearly delineated’ is used as a matrix to map the ‘less clearly 
delineated’ upon, thereby deeply influencing the way we understand the latter.6 CMT thus argues 
that the words we encounter, the concepts we process, and the ways in which we process these 
are grounded in our embodied lives. The question before us now is this: how would CMT explain 
syllogistic reasoning and the phenomenon of circling? 

 
Engaging with premises, and drawing inferences from these, is obviously a matter of 

engaging with words and sentences. Contrary to cognitivism’s account, these words and sentences 
do not get encoded into amodal representations, but they get encoded into modal representations 
(which means that they are somehow constitutively, instead of just causally, connected to, or 
shaped by, our sensory experiences).7 They recruit cortical systems for kicking, seeing, touching, 
and moving in general, even if they have to go through some metaphorical mapping. To get a 
better idea of what actually happens (what ‘the recruitment’ of cortical systems in this context 
means), and to understand what circling has got to do with syllogistic reasoning, we’ll have to 
take a closer look at what happens during reasoning tasks, according to psychological research. 

 
Let us take [1], the syllogism we discussed in the Introduction as an example. A subject first 

gets to accommodate the first premise, “No human is a mammal.” The subject will process the 
premise into some kind of representation. Second, the subject has to take the second premise 
and integrate that information into the representation of the first premise (Johnson-Laird 2001). 
Thirdly, and crucially, the actual reasoning part starts: what conclusion follows, if any? Taking 
CMT’s cue, we can see how words like ‘mammal,’ and ‘human’ get encoded with concepts like 
MAMMAL and HUMAN. These are grounded, according to CMT, and sensorimotor systems 
are recruited for their processing. That explains why reasoners often report visualizing the 

 
6 Gallese and Lakoff argue that the same neural networks involved in processing the source domain, are recruited to 
process the target (Gallese and Lakoff 2005). The source schema has a structuring influence on the target; the target 
gets molded into the format of the source (that is what ‘mapping’ means). Our understanding of the structure of 
space, for instance, molds our understanding of the structure of time, to the point that we cannot untangle TIME 
from its spatial schema. Because we recruit the neural circuitry created by, and for, embodied experiences to deal 
with concepts, we think, infer, manipulate, and process all concepts in an embodied way. Thinking about the passing 
of time is based on the same structure in which we think about space, with this latter structure thoroughly grounded 
in our bodily capacities and embodied experiences.  
7 Unlike some of the more radical versions of 4E (e.g. Hutto and Myin, 2017), I condone the talk of ‘representations’, 
as long as we don’t consider them to be things we can point at (cf. Zahnoun, 2021). More precisely, I agree with the 
criticism targeting the ‘reification’ of representations, turning them into entities that might be acceptable for any 
natural science, while they retain their magical semantics. In this paper, however, I have chosen to follow mainstream 
psychology, and liberally use ‘representations’, without claiming that I know what they precisely are supposed to be.  



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situation that is stated by the premises: concepts like MAMMAL are ‘seen’ in the mind, and the 
premises state a situation in which mammals and humans are seen as distinct groups (Bucciarelli 
& Johnson-Laird, 1999). 

What happens in the third, essential, step? Even though some test subjects report using the 
rules of inference, and other test subjects report on ‘seeing’ the validity in the mental picture they 
have created, it can be argued that both reports do not report what happens on a more basic level. 
When people experience rule-following, they might be using some kind of formal operation, but 
it’s hard to say what that actually looks like for a reasoner. How does one understand that humans 
and mammals are disjunct, for instance? This strategy also wouldn’t explain the fact that some 
types of syllogism (for instance, categorical) are easier than other types (for instance, disjunctive). 
These types rely on the same number of rules. Reports on ‘seeing’ the scene, and being able to 
derive conclusions that way, are also highly unlikely. Markus Knauff has demonstrated that in 
such reasoning, visualization actually impedes reasoning performance (Knauff, 2013). This visual 
impedance effect is, in all likelihood, caused by working memory overload, caused by irrelevant 
visual details. It also doesn’t concur with neurological findings. Fangmeier et al. found that during 
the first two steps visual areas are activated (along with memory-related areas), but that these cease 
all activity in step 3. In step 3 the posterior parietal cortex becomes active, especially those areas 
that are associated with dealing with spatial challenges (Fangmeier et al., 2006). Using 
Transcranial Magnetic Stimulation (in which the functioning of specific cortical areas is 
hampered), Hamburger et al. found that targeting the primary visual cortex (V1) caused people 
to reason better (Hamburger et al. 2018). In sum, reasoners don’t reason by following logical rules, 
and they don’t reason by manipulating imagistic representations. 

 
Knauff and collaborators came up with an alternative explanation. The neurological data 

suggests that spatial skills are essential in step 3. Behavioral data suggest the same: concurrent 
spatial tasks impede reasoning, while concurrent visual, computational, or linguistic tasks, do not 
(Knauff et al. 2004). Knauff therefore develops the Space to Reason Theory (SRT. Knauff, 2013), 
which claims that reasoning is basically a spatial activity. Let’s look at step 3 of evaluating [1] and 
see what happens according to SRT. When reasoners disjunct MAMMAL and HUMAN, they 
create a so-called spatial layout. Spatial layouts abstract away from irrelevant detail, but 
schematically structure the situation, based on the relevant features of the premises.8 In other 
words, reasoners (unconsciously, because this happens in the parietal cortex, which is inaccessible 
to human consciousness) create a semi-abstract arrangement in which the stated situation is 
expressed by spatial relations. Semi-abstract sets MAMMAL and HUMAN are spatially separated 
from each other.9 Evaluating the conclusion of [1] then requires a spatial judgement: the 
conclusion is a spatial overlap between MORTAL and MAMMAL. If such an overlap is 
necessitated by the premises (meaning that the spatial layout couldn’t have been different), the 
conclusion is valid. Let’s take [3], slightly more accessible than [1]: 

 
[3] 1. All humans are mammals 

 
8 That irrelevant detail can get in the way, can be illustrated by adorning [1] with all kinds of adjectives. E.g. “None 
of the purple-haired humans is a furry and warm mammal. All creatures that are human, have ears, and that 
sometimes are furry and warm, can die. Therefore, some of the animals that have ears, are sometimes purple, but 
not furry and warm, are mortal.” 
9 This is what a disjunction looks like, and probably is the only real phenomenological experience people can have 
when thinking about disjunct entities. 



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 2. All mammals are mortal 
 
Therefore 
 

3. All humans are mortal 
 

In tackling [3], a reasoner spatially arranges HUMAN to be a subset of MAMMAL, and 
MAMMAL to be a subset of MORTAL. Judging validity now becomes a matter of judging 
containment. The premises, as grounded propositions, thus recruit the cortical systems that also 
enable spatial skills, which are based on our extensive experience with containment. Looking 
back at the argument from evolution we discussed earlier, that makes sense: phylogenetically and 
ontogenetically, we learn to deal with three-dimensional space much earlier than we learn to deal 
with linguistically presented premises and conclusions (Godfrey-Smith, 1996). It is very likely that 
dealing with deducing is a case of exaptation (Gould and Vrba, 1982): evolutionary adaptation 
works too slowly to have created specialized structures for this job, so, as a matter of neural reuse, 
an existing structure was recruited to do the job (Anderson 2010). In exaptation the older 
structure typically influences the new function, much like what happens in CMT’s mapping 
relations. Mark Johnson links this to a naturalized theory of language. This theory 
 

is based on the hypothesis that, over the course of evolutionary history, humans developed the 
capacity to recruit areas of the brain originally evolved for perception and motor activity for the 
purpose of “higher”-level acts of conceptualization, reasoning, and linguistic communication. 
Exaptation—the technical term for this type of process—is used to explain how embodied creatures 
could possibly acquire abstract thought and expression by making use of the body-based syntax 
and semantics of perception and bodily action. (Johnson, 2018: 634) 
  

Our linguistic skills are realized by cortices that were adapted for dealing with being an embodied 
creature, living in a three-dimensional world, linking our concepts to embodied capacities, skills 
and experiences. Deducing is grounded in cortices that were adapted to deal specifically with 
space, and therefore deducing is infused with spatiality, and therefore syllogistic reasoning relies 
on spatial layouts. 
 

So, what about the diagrams? We noticed that using diagrams enhances syllogistic skill, 
even when diagrams are ‘merely’ mentally manipulated. We also noted that cognitivism’s 
explanation of this phenomenon, which is based on cognitive offloading, doesn’t do the job it 
wants to be done. Let’s look at an embodied account of physically handling Venn diagrams 
(usually by drawing). When a subject reads premise 1. from the example we discussed in the 
Introduction, “No human is a mammal”, the contents get processed into representations of two 
sets, or groups. Premise 1 states that these groups, group HUMANS and group MAMMALS, are 
distinct, meaning that they do not overlap. ‘Grouping’ and ‘overlapping’ seem to be only 
figurative (metaphorical) ways of describing what happens, but the claim of this paper is that the 
premise actually gets encoded into a spatial format, that is, gets configured by image schemas into 
a quasi-abstract representation. The subject thus creates a spatial arrangement of two groups 
separated by space. When the subject draws [4], she expresses this internal layout. 

 
 



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[4]    

Humans   Mammals 

 
 
When engaging in the second premise, she spatially includes HUMANS as a group inside a 

third, larger, group, namely group MORTAL. In doing so, she notices that the situation affords 
more than one spatial layout, as in possibilities A, B, and C we drew in the Introduction. We 
already saw that the indeterminacy of that example makes the offered conclusion invalid. 

 
Cognitivism’s account of circling when drawing might be just as good as the one offered 

above. Drawing diagrams might, after all, be a case of cognitive offloading. It is in the explanation 
of purely mental circling (‘in the mind’s eye’) that cognitivism is less convincing. Cognitivism 
basically claims that people who have had some experience with drawing diagrams internalize this 
tool by visualizing the circles. In doing so, they get -at least some of- the effect of external tool-use 
on syllogistic skill. The embodied account turns the story around; circling isn’t a tool to alleviate 
cognitive load, but understanding syllogisms is circling. Paying attention to visual imagery, or 
trying to follow rules of inference, merely distracts from the actual mechanism that enables us to 
tackle syllogistic tasks. Drawing is thus not a spatial expression of the processing of symbolic 
representations, but the outward expression of modal (i.e. spatial) processing. Circling is already 
part of the internal processing, and is therefore not something that one internalizes, but 
something one externalizes when actually drawing. The reported internal visualization of 
diagrams is therefore effect and does not cause syllogistic skill. 

 
The phenomenon that experiences with physically using diagrams (i.e. by drawing) 

enhances syllogistic skill is caused by the structuring effect the experience has: experiencing spatial 
layouts in syllogistic tasks creates a -more or less- noise-free approach (Knauff, 2013). The 
sensorimotor experience activates the cortical systems dedicated to spatial activity directly, and 
thus creates neural pathways between linguistically rendered premises and spatial layouts. The 
experience affects the way one sets up a cognitive system: the more efficient such pathways, the 
more efficient the reasoner (see Lakoff 2014, for a non-technical description of the build-up of 
neural pathways as the substrate for metaphorical mapping). 

 
In sum: the embodied account of syllogistic reasoning developed here argues that a reasoner 

tackles syllogistic tasks by recruiting systems that we also (and primarily) use for dealing with 
space. These systems influence our reasoning processes by molding them into a spatial format. 
The efficiency of such spatial formats can get impeded by distractions, but sensorimotor 
experience with spatial formats trains the reasoner in discerning relevant aspects. This accounts 
for the role of Venn diagrams in the enhancement of syllogistic skills. 

 
Section 3 describes a test that I developed to look for the structural link between embodied 

experience and syllogistic performance. In Section 4, I discuss possibilities to use the setup of the 
test for teaching practices. 
 



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3. Testing Whether Enhanced Bodily Experience Enhances Syllogistic 

Performance 
 

If the argument developed in this paper is right, and if conventional wisdom on training 
and practice is right, a richer (longer, or more intense, or multimodal) experience will yield more 
results. If we, therefore, enrich the bodily experience of engaging with Venn diagrams, we should 
further enhance syllogistic skills. If this is what we see, cognitivism will have a hard time 
explaining it. It would be hard to sustain that there’s no constitutive role for embodiment if there 
is a structural link between embodied experience and syllogistic skill. To test this, I created 
cardboard circles that can be used as 3D Venn diagrams. Handling these will surely create a 
multimodal experience (visual, tactile) that should, if the embodied view is right, enhance 
performance more so than ‘mere’ drawing, because the reactivation of spatial skills will be 
stronger, and the neural pathways will get stronger. 

 
We selected test subjects who are unlikely to have had experience with using diagrams in 

syllogistic reasoning, but who are cognitively advanced enough to be able to evaluate syllogisms. 
Our test subjects were therefore 3rd grade high school pupils, from pre-university level secondary 
education, at a school that intends to supply pupils with a broad intellectual education, including 
classical Greek and Roman languages and culture. This school also offers approximately 20% of 
the schedule’s time to projects that are - mostly - not part of the compulsory curriculum. Getting 
introduced to syllogisms is thus embedded in the school’s ambition and program. These pupils 
also haven’t had any experience with syllogistic reasoning, as far as we know (it’s not on the 
school’s schedule in grades 1 to 3, and during the experiment none of the pupils gave any sign of 
having prior knowledge). 
 
Test subjects: 77, average age 14 years old, approximately equally composed of male and female, 
predominantly native Dutch. 
Location: pupil’s own high school (Netherlands), 4 classrooms.  
Date: June 23rd, 2023. 
 

We told the pupils that we were giving them training in syllogistic reasoning. We labelled 
4 groups, A, B1, B2, and C (24 in A, 15 in B1, 21 in B2, and 17 in C). We used their regular 
grouping (these groups are randomly created when entering 1st grade, by dividing the total 
number of new pupils into groups of roughly equal size. The difference between the numbers of 
pupils in these groups during the test was almost wholly caused by absentees). The 4 groups were 
separated and supervised by 4 qualified high school teachers. The test ran as follows: 
 
Round 1 

  

- Group A got to watch an instructional video on syllogisms (4 minutes), in which there is 
no mention of diagrams. The video focusses on discerning valid from invalid conclusions. 
The attendant teacher was instructed to refrain from suggesting diagrams, or any other 
technique. The subjects got several syllogisms to practice with, for 60 minutes, supervised 
by the attendant teacher. Then, they took Test 1, consisting of 10 syllogisms, with 3 



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invalid and 1 valid conclusion per syllogism offered, in a 10-minute frame.10 They got to 
use a draft sheet. They ticked their answers on a multiple-choice response form.  
 
 

[5] Examples Tests 1 and 2:11 

 
Given: All bears are made of wood  
Given: Some bears are sharp 

 All sharp things are made of wood   

 At least some sharp things are made of wood  

 No sharp thing is made of wood 

 No wooden thing is sharp 
 
Given: No A’s are B's 
Given: No B’s are C's 

 All A’s are C’s 

 No C is an A 

 Some A’s are C 

 Nothing follows 
 

- Group B1 and group B2 got to watch an instructional video on syllogisms (5 minutes), in 
which the use of Venn diagrams is explained. The video focusses on discerning valid from 
invalid conclusions. The subjects got several syllogisms to practice with, for 60 minutes, 
supervised by the attendant teacher. Then, they took Test 1. They got to use a draft sheet. 
They ticked their answers on a multiple-choice response form. 
 

- Group C got to watch an instructional video on syllogisms (5 minutes), in which the use 
of the 3D Venn diagrams is explained. The subjects got sets of cardboard circles, and 
syllogisms to practice with, for 60 minutes, supervised by the attendant teacher. The 
cardboard circles were concentrically laser cut from thick paper (basically as thick as the 
machine can cut without seriously burning the paper; in our case we were satisfied with 
120g paper). Their rims allow writing (to denote the set), come in different diameters (the 
A3-sheets they are cut from allow circles of up to 40 cm), and can be laid out in distinct, 
overlapping, or including patterns. Figure 1 illustrates the use of the circles (in this case a 
hand-cut version) for the valid “All men (mensen) are animals (dieren), All animals are 
mortal (sterfelijk), Therefore all men are mortal”.  

 

 
10 The training set, Test 1, and Test 2 were created by randomly selecting (through an online bingo machine: 
https://basisonderwijs.online/digibordtools/bingo.html) 3x10 syllogisms from a large collection of syllogisms.  
11 This is a translation: the tests were taken in Dutch. 



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[Figure 1] 

  
 
Figure 2 gives the three possible layouts of the invalid syllogism “All men are animals, 
some animals are mortal, therefore some men are mortal”. Notice that the layout on 
the right shows the invalidity: the premises allow this third layout, therefore the 
conclusion does not follow of necessity.  
 

[Figure 2]  
 

   
 
The pupils in this group found out that they had to think about the sizes of the sets. 
Randomly assigning cardboard circles to sets created problems, as when, in above 
example, they assigned ‘men’ to a big circle, and ‘animals’ to a smaller one. As soon 
as they figured out how to use the correct sizes, they started to stack and slide the 
circles. After some practice, they could determine which layout(s) matched the 
premises, and, as several pupils said, they could ‘see,’ or ‘read off,’ whether the 
possibilities validated the conclusion. For instance, they pointed at the layout at the 
right of Figure 2 and stated that ‘men’ and ‘mortal’ do not have to ‘overlap,’ rendering 
the conclusion invalid. It seems as though they understood disjunction through the 
experience of circles that do not have a shared space.  
 

After practice, they took Test 1. They got to use the cardboard circles. They ticked their 
answers on a multiple-choice response form. 

 



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An incentive was built in, the subject of the group who did best receives a prize (a bag of 
candy). Speed decided who won in case of a draw. This was mentioned at the beginning of Round 
1. 
 
Round 2: 

 
- After a short break (10 minutes passed in the classroom to prevent communication 

between the groups), all test subjects took Test 2, consisting of 10 syllogisms, with 3 
invalid and 1 valid conclusion per syllogism offered, in a 10-minute frame. They only got 
a response form, without being allowed to write or draw (it was made explicit that any 
marks other than name and ticked answers would render the test invalid). Incentive for 
all groups: the subject per group who made the most progress (as compared to Test 1) 
receives a prize (bag of candy). This was mentioned at the beginning of Round 2. 
 

After the test all response forms were anonymized, and the results compiled and checked 
for the hypotheses.  
 

We suspected that the format of the tests would influence the results: for group A, practice 
and Test 2 resemble Test 1, meaning that practice and Test 1 align with Test 2. For groups B1, 
B2, and C, Test 2 would be in a novel format, not aligned with practice and Test 1. We therefore 
suspected that group A would get better results at Test 2, and the other groups would, being 
deprived of their tools, get worse results. After all, it is unlikely that 60 minutes of practice and a 
10-minute test will enhance skills enough to cancel this misalignment effect. Crucially, we 
hypothesized that group C would get worse results, but significantly ‘less bad’ than groups B1 and 
B2.  
 

It turned out that group A indeed improved their average performance: the score (number 
of correct answers, out of the 10 requested) went up 0.67 points from Test 1 to Test 2. Group B1 
scored worse on Test 2, by 0.87 points. Group B2 also scored worse on Test 2, by 1.19 points. 
These findings were in line with our expectations. However, group C’s score went up on Test 2, 
by 0.71 points.  
 
 [6]  

 
 
 
 
 
 
 
 
 
 

At first glance, unguided teaching seems to be most effective. The group that didn’t get any 
instruction, other than ‘determine the validity’, Group A, outperformed the other groups in both 
tests. However, as teachers know, groups develop their own dynamic, and Group A seems to be 

Group Test 1 Test 2 Difference 

A 6.13 6.79 0.67 

B1 6.07 5.20 -0.87 

B2 6.10 4.90 -1.19 

C 6.06 6.76 0.71 



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a more focused, and hence more successful group of pupils. Average grades (across all school 
subjects) in Group A (which is, as noted, a regular class) are approximately 0.6 points (on a 10-
point scale) higher than grades in Groups B1, B2, and C. This would explain the results of Test 
1. Group A also outperformed the other groups on Test 2, by improving their score by 0.67 
points. However, if we take the misalignment effect into account, and see what that effect causes 
in Groups B1 and B2, we could add that score to Group C’s score on Test 2. In other words, 
Group C’s skills cancelled the misalignment effect, leading to affecting the most progress from 
Test 1 to Test 2. It might be argued that the 3D diagrams were ‘less misaligned’ than the 2D 
diagrams, but that would only contribute to the embodied account that this paper develops.  
 

4. How Teachers Can Encourage Spatial Actions in Syllogistic Reasoning 
 

If, as I’ve argued in the Introduction, teaching syllogistic skills is worth your pupils’ while, 
the embodied (cardboard) system seems to offer an effective way of doing so. In this section, I 
will give some guidelines on how to use the cardboard system.  

 
Preparation: 

 
• Consider your goals and your program: how much time are you willing to spend on the 

honing of this skill? At this time, I haven’t investigated whether the effect of the carboard 
circles lasts, but didactical wisdom tells us that training a skill should, ideally, be a 
prolonged, recurrent, or at least repeated, affair. Trying to organize such training might 
cause practical problems. Typical high school timeslots don’t allow prolonged training 
sessions, so you might want to plan several sessions. This might also be the point at which 
to think about how much time you are willing to spend on teaching syllogistic skills. I 
started this paper with arguing that syllogistic reasoning is a good starting point to start 
honing reasoning skills, and that reasoning skills in natural language are the backbone of 
critical thinking. However, there is a curriculum at every school, and there simply isn’t 
enough time to do everything. It might be argued that pupils learn reasoning skills when 
they’re integrated into other subjects: applying them to the subject at hand makes those 
skills seem to be more relevant, and valuable time would be saved. However, making the 
training of syllogistic reasoning a distinct part of your program highlights it as a skill that 
can be applied to all kinds of reasoning challenges, instead of it being just applicable to 
the subject at hand. We are all familiar with the effects of compartmentalization in 
educational practices: transfer is hindered when the principles of the skill are not 
explicitly addressed (Billing, 2007). It seems advisable to devote at least some time to the 
explicit teaching and training of the key skill of syllogistic reasoning. 
 

• It is required that your pupils have a rudimentary grasp on what validity is (and know how 
to distinguish it from truth; in my experience younger pupils find it hard, at first, to accept 
the validity of false conclusions). Teaching them how to work with validity is, of course, a 
matter of using the circles. 
 
 



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• Consider how many syllogisms you want them to tackle and decide on the number of 3D 
circles per pupil. Note that they need a set of several (at least three) circles per syllogism. 
Anything circular that you can carry around by the dozens, and that’s preferably reusable, 
will do. However, I tested several plastic circles (acrylic glass, among others), but ran into 
the problem that most plastics are sensitive to the solvents in (erasable) markers, and 
quickly become messy when (re)used. Besides having limited reusability, they’re expensive 
(compared to paper), and quite heavy if you need a hundred or more. As said, I ended up 
using a laser cutter and paper to make a stack of circles. Whatever your material of choice, 
be sure to carry extra circles, because your pupils are bound to lose, mess up, or break a 
few.  
 

• Find or create a training set of syllogistic challenges. They’re quite easy to find online and can 
also be diligently constructed.12 Once created or found, you might want to sort them in 
degree of difficulty (syllogistic modus, order in which premises are presented, with or 
without valid conclusions, counterfactual, abstract, etc.). You might want to use abstract 
items only, to make your training less dependent on world involving knowledge, and 
therefore more culturally inclusive. 
 

• Decide on a set-up: do you want the pupils to cooperate, or to work alone? How many 
demonstrations are you going to use? How much guidance are you willing to provide? 
What do you plan to do when pupils prefer to indicate different strategies and tools?  
 

Execution: 

 
• As any teacher knows, making the relevancy of the task at hand explicit for the pupil helps 

in motivation. Showing that everyday life is rich in syllogistic reasoning and illustrate this 
with a score of common and recognizable mistakes, and maybe even with examples of bad 
and downright deceptive arguments. For older pupils, it might help to argue that 
academic success -partly- depends on reasoning skills, and that syllogistic reasoning is part 
of most formal assessments. 
 

• Be sure to create a safe atmosphere: pupils might come to perceive your setup as an 
intelligence test. Stress that reasoning is a skill that one gets better at through practice. 
 

• You could tell them about the theory behind the use of cardboard circles, but it will not 
further your goals, because the pupils cannot consciously activate spatial pathways in the 
parietal cortex. Tell them that working with the tokens improves reasoning skills, and that 
those skills carry over to reasoning without the tokens. Demonstrate the use by example.  
 

 
12 And, of course, you’re welcome to my sets (in Dutch). 
 

 

 
 



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• If you have planned enough time, take a baseline test at the start, and a test at the end of 
your training session(s). This will provide extra motivation. It is highly unlikely that a 
pupil will do worse at the second test, and learners enjoy progress. If your training set allows 
it, creating short tests is quite easy, and pupils can easily score their own results. 
 

• You might be able to plan another training session, and you might be able to point at 
syllogistic reasoning in your further curriculum. Both are highly advisable for retention of 
the enhanced skill.  

 
5. Conclusion and Discussion 

 
This paper has argued that a convergence of research shows that syllogistic reasoning is a 

spatial activity, even if such reasoning has traditionally been seen as rule-following or the 
manipulation of mental images. That suggests that priming the activation of spatial capacities 
should enhance syllogistic performance, and that such priming could be a way to effectively teach 
syllogistic skills. A pilot experiment, that was conducted to see if such a priming effect could be 
seen, pointed toward the viability of this paper’s argument. 

 
However, the results of the experiment should not be accepted unconditionally: the setup 

omitted a baseline test, and a test with 77 subjects has limited value. Other factors might have 
influenced the results: working with the cardboard circles created a cheerful atmosphere and 
having fun while learning could be a cause of improved results. What I called the ‘dynamic’ of 
groups might also have influenced the results: not all groups applied themselves in the same way, 
and their focus might have shifted between Test 1 and Test 2. There are doubtlessly more factors 
influencing the outcomes, causing noise for the interpretation. Still, the experiment, as 
something of a pilot study, seems to point at the viability of the embodied account of syllogistic 
reasoning. In cognitivism’s view, the apparent fact that tackling syllogisms by handling three-
dimensional circles enhances skill is hard to explain. Cognitivists view this skill as a disembodied 
skill, aimed at the manipulation of symbols. Therefore, lifting and stacking pieces of cardboard 
cannot contribute to such a skill, let alone more so than drawing on pieces of paper. However, the 
embodied view can elegantly explain the results of the test. 

 
The argument and the experiment suggest that working with the 3D circles can be effectively 

used when teaching syllogistic skills. In Section 4, I’ve tried to sketch how embodied reasoning 
can be implemented in educational practices. However, the proof is in the eating of the pudding, 
and other attempts to apply the cardboard system might debunk both the argument for embodied 
reasoning, and the claimed value for teaching. I am, of course, very much hoping that colleagues 
will try out what I’ve sketched, and will find an effective tool for teaching, and, simultaneously, 
corroborate my argument.  
 
 

 

 

 

 

 



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Address Correspondences to: 
Menno van Calcar, 
Erasmus School of Philosophy, Rotterdam 
Email: vancalcar@esphil.eur.nl 

 

mailto:vancalcar@esphil.eur.nl

