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A Model of Philosophical Discussion in the Classroom 

 
 
Philip Cam   
 
 
Abstract 
A general conception of discussion and its relation to the development of reflective thinking is applied to 
philosophical inquiry in the classroom. Consideration of what makes a discussion philosophical is used to 
reveal the kind of thinking involved and then set within a model of discussion for the classroom designed to 
engage students in it. It is shown how a range of questioning, conceptual exploration, and reasoning tools can 
be introduced within that framework that will improve students’ capacities to think both critically and 
creatively.     
 

  
eing asked to write something on my contribution to philosophy in schools presents a 
dilemma. My interests have ranged from creating books of philosophical stories for 

children with accompanying exercises and activities, to writing books for teachers and running 
workshops, as well as spending a good deal of time writing about issues in educational theory, with its 
decidedly academic appeal.1 It is not easy to sum all that up, except perhaps to advocate this mixture 
of theory and practice in the message that I would like to pass on. To rework Immanuel Kant: 
Without educational practice, we would have nothing to theorize about, but without theory we would 
have no considered idea of what education is all about. Educational theory without practice is empty, 
but educational practice without theory is blind.2   
 

This may cover the general tenor of my remarks, but I must fill them out with something in 
particular. Since I have long been interested in the ways in which thought and speech operate in 
collaborative philosophical inquiry, I have chosen to focus on it. That will give a somewhat theoretical 
cast to the essay, but let me immediately point out that I will treat it as continuous with the question 
of how to make the most effective use of these operations in the classroom. In going back over this 
territory, I hope to provide a serviceable map of the terrain for teachers who lead children into it.  

    
I am going to start with a general conception of discussion and its connection with reflective 

thinking and then home in on what makes a discussion philosophical and the kinds of thinking that 
it involves. I will go on to apply these general conceptions to philosophical inquiry in the classroom 
and show how various cognitive operations and speech acts function within it. From this I will extract 
a kit of tools for use in questioning, conceptual exploration and reasoning, which can be used to 
strengthen educational outcomes.    
                                                 
1 I have included only a couple of these works in the references. A complete list of books and articles can be found on my 
website https://www.philipcam.com  
2 “Without sensibility no object would be given to us; and without understanding no object would be thought. Thoughts 
without content are empty: intuitions without concepts are blind.” Immanuel Kant, Critique of Pure Reason, A 51, B 75.    

B 

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Discussion and the Development of Reflective Thought 
 

We may think of a discussion as a deliberative conversation that addresses a question or 
problem in a systematic way. Let us consider the terms of this definition. First, we have conversation, 
which is a verbal exchange between two or more people. Conversations include the exchange of such 
things as news, opinions, observations or ideas on one or more topics. Sometimes the conversations 
we engage in are deliberative. In these cases, we take pains to examine things and think them through. 
We may do so when planning a course of action, say, or coming to a considered judgment. When a 
deliberative conversation is sufficiently focused and structured to become a systematic examination of 
a problem or question, it is what I am calling a discussion.  
 

The connection between deliberative conversation and individual deliberation has often been 
drawn. It is at least as old as Plato. In the Theaetetus, he has Socrates suggest that “the soul when 
thinking appears to me to be just talking—asking questions of herself and answering them, affirming 
and denying”, it being a “conversation which the soul holds with herself in considering of anything” 
(Plato, Theaetetus 190a). It has also informed conjectures as to the origins of reflective thought. Here is 
John Dewey: 

 
No process is more recurrent in history than the transfer of operations carried on between 
different persons into the arena of an individual’s own consciousness. The discussion 
which at first took place by bringing ideas from different persons into contact, by 
introducing them into the forum of competition, and by subjecting them to critical 
comparison and selective decision, finally became a habit of the individual with himself. 
He became a miniature social assemblage, in which the pros and cons were brought into 
play struggling for mastery—for final conclusion. In some such way we conceive reflection 
to be born (Dewey, 2004, p. 123). 

 
When it comes to the development of reflective thought in the individual, it is worth recalling 

that this idea is but a special case of the central proposition of Vygotskian developmental psychology, 
that cognition, in all its higher forms, is an internalization of social interactions:  

 
Every feature in the child’s cultural development appears twice: first on the social level, and 
later, on the individual level; first between people (interpsychological), and then inside the 
child (intrapsychological). This applies equally to voluntary attention, to logical memory, and 
to the formation of concepts. All the higher psychological functions originate as actual 
relations between human individuals (Vygotsky, 1978, p. 57.).  

 
The educational implication of these remarks is clear. If we want students to develop the ability 

to think about things for themselves, we need to place a premium on discussion. To take just a couple 
of points by way of illustration: Having students engage in the give-and-take of reasons in discussion is 
the forerunner of individuals coming to explore the pros and cons of suggestions that arise in their 
own minds. Considering different people’s viewpoints during discussion helps to seed the habit of 
students looking at things from different perspectives in their own thinking.   
 



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Having defined what I mean by discussion, connected it with the capacity for reflection, and 
drawn attention to the educational role that it may play, let’s now turn to what makes a discussion 
philosophical and the kinds of thinking that it involves.  

 
Philosophical Discussion and the Kinds of Thinking It Involves 
 

As with discussion more broadly, philosophical discussion addresses problems or questions, and 
we may begin to say what makes a discussion philosophical by looking at their general characteristics.  
Open a standard introduction to philosophy and you will find problems and questions regarding such 
things as knowledge, existence, society, morality, aesthetics, and religion.  As a general procedure, the 
problems of philosophy are tackled by addressing the questions that they raise. To take a couple of 
traditional examples: there might be an attempt to resolve the mind-body problem by addressing the 
question whether mental states can be identified with states of the brain; or again, the problem of 
freewill and determinism might be addressed by starting with the question of what it means to say that 
a person could have done otherwise. 
 

While philosophy’s problems and questions vary widely in their subject matter, they all have to 
do with abiding human concerns. What constitutes knowledge and how it differs from belief and 
opinion, for example, concerns us all, and is no small matter, given the claims to knowledge 
constantly pressed upon us. This extends to the scope and propriety of all our attempts to gain 
knowledge of the world through science, religion, literature and art. The same point can be made in 
regard to the moral and legal realms. The question whether we should judge a person’s actions by 
their intention, by their consequences, or some other standard, has a profound bearing on judgments 
made in everyday life, as well as within institutions such as the law. 
 

It is important to note that these matters cannot be settled simply by an appeal to the facts, or 
any kind of scientific method. This is not to say that such means are irrelevant. The results of 
psychology and brain science are certainly relevant to the mind-body problem, for example, but their 
bearing cannot be judged without a good deal of analysis and argument.  Similarly, it is just possible 
that physical indeterminacy at the quantum level may have implications for thinking about the 
wellsprings of freely chosen human action, but there is no shortcut from physical theory to a 
settlement of that perennial problem.  
 

This does not mean that, beyond consistency with what we otherwise know, one response is as 
good as another. As in many things, our responses can be clear-headed and insightful, or muddled-
headed and obtuse. Even when they have attained the status of received opinions, however, they 
remain open to challenge; and accepting the settled opinions of previous generations on such matters 
can mean living with outdated ideas. The once widely accepted view that the mind is an entity 
metaphysically distinct from the body has come to be contentious, to say the least, as has the oft 
accompanying belief that human beings have a free pass to intervene, as it were from the outside, in 
the causal fabric of the world.  

 
This brings us to two ways in which philosophical problems and questions typically call for a 

response. One is that they invite conceptual investigation. Aside from straightforwardly conceptual 



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questions, which are common in philosophy, the need for conceptual exploration characteristically 
extends to the terms in which philosophical problems and questions are posed. Thus, we need to be 
clear about what we understand by the mind, or mental states and processes, in order to bring the 
available evidence to bear on the mind-body problem. In regard to the suggestion that quantum 
indeterminacy may help us to solve the problem of freewill and determinism, how clear is it that the 
conception of freely choosing to do something can be made sense of in terms of indeterminacy? 
Unless the terms in which our questions and problems are stated are in good order conceptually, we 
will not make much progress.  
 

The other thing that philosophical problems and questions usually demand is a good deal of 
careful reasoning. Tracking down the implications of theories and suggestions to see how they fare is 
no less a matter of methodical investigation than it is in scientific inquiry. The claim that 
consciousness might be a physiological process occurring in the brain, for instance, needs to meet a 
good number of objections, which have, in fact, produced a considerable literature. Again, only a 
good deal of careful argument from physical theory via physiological psychology to what we know 
about the wellsprings of human action could have any hope of making a convincing case for quantum 
indeterminacy to underwrite free action in an otherwise deterministic world. 
 

Given this, it should come as no surprise that philosophy has done a great deal to develop these 
two methods of investigation. Conceptual exploration is at least as old as Plato’s Dialogues, while 
systematic attention to reasoning goes back to Aristotle. These things have developed over the history 
of philosophy and become fashioned into conceptual and logical tools that have widespread 
application, not just in philosophy. This is a point of particular interest. In my view, it is their wide-
ranging utility that strongly commends them when it comes to general education. After all, education 
is not just a matter of acquiring subject knowledge, but of learning to think about it. It is an 
apprenticeship in learning to use the tools of thought to do the job that they are designed to do. 
 

Although they are fit for general use, the best way of acquiring these tools is to engage in 
philosophical inquiry, where their application is front and center. Bearing in mind what was said 
about the connection between discussion and the development of reflective thought, it is to 
philosophical discussion in particular that we should turn. This is the way to develop general thinking 
capabilities that can be applied across the curriculum. 
 

Before moving on, I should draw attention to the attitude appropriate to philosophical matters. 
While I have been focusing on the character of philosophical problems and questions, philosophical 
inquiry depends upon treating them in a philosophical way. After all, it is possible to adopt a different 
stance to the kinds of problems and questions with which philosophy deals. One might regard such 
matters as answered by appeal to authority, for example. Depending on the case, that might mean 
falling back on received opinions, religious teachings, parental values, or looking to the teacher for the 
‘right answer’.  
 

Adopting a philosophical attitude to some matter is appropriate where that enables us to see it 
as it should be seen—that is to say, as open to discussion and the application of philosophical method. 
While other problems and questions call for other attitudes, such as the scientific and the aesthetic, 



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knowing when to adopt a philosophical attitude is primarily a matter of being able to recognize 
philosophical problems and questions through the characteristics mentioned above.   
 
Application to the Classroom 
 

In order to understand how the tools of philosophical inquiry operate, it is best to place them in 
the context of their use. For us, that means philosophical discussion in the classroom. Whatever 
complexities and messiness might appear on the surface of any such discussion, we should not lose 
sight of its underlying form. Let us examine it briefly, setting out the steps in the process and the 
means being employed at each stage. 
 
 
 
       STIMULATING 
 
 
 
ESTABLISHING AN AGENDA 
 
 
 
        SUGGESTING 
                           
 
REASONING & ANALYSIS 
                        

    EVALUATING 
 
 
      CONCLUDING                                                                            
 
 
 
 
 

John Dewey says that inquiry begins with a felt difficulty that arises in a problematic situation, 
whether in everyday life or in intellectual pursuits (Dewey, 1991).3 Whatever the subject under 
discussion in the classroom, this is likely to require the teacher to introduce some suitable stimulus 

                                                 
3 Dewey’s account of inquiry in How We Think is a reworking of his understanding of scientific inquiry, aimed at teachers. 
My account is itself a reworking of Dewey for the purposes of philosophical classroom discussion. For an overview of 
Dewey’s model, see especially pp. 72-78 of How We Think.   

Problems or issues 
and questions concerning 

them 
 

Implications 
Assumptions 

Evidence  
Criteria  

Counterexamples 
 

Initial 
problematic 

situation 

Ideas 
Conjectures 
Hypotheses 

Conclusion 
Resolution 

Implementation 

__
__

__
__

_C
re

at
iv

e 
Ph

as
e_

__
__

__
__

 
  

__
__

__
_C

rit
ic

al
 P

ha
se

__
__

__
_ 

 
The teacher introduces 

stimulus material 
 
Students identify problems or 
issues and raise questions for 

discussion 
 

 

Students consider some 
matter and make suggestions 

 

Students evaluate their 
suggestions by analysing 
them and exploring their 

implications  

 

Students make conclusions 
and reflect on them 



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material. That is to say, material that problematizes something in the curriculum with the aim of 
stimulating Dewey’s “felt difficulty” in order to motivate inquiry.  

 
A problem or issue is one thing, its articulation is another. Having become aware that there is 

something worth looking into, the first step in dealing with it is to identify the nature of the problem, 
or say what is at issue. After all, we need to know what we are inquiring into. Failure to understand 
the nature of the problem or to see what is at issue is a sure-fire way of going wrong. Apart from being 
integral to inquiry, it is important for students to be able to identify problems for themselves, and not 
have teachers and textbooks forever set them, as if they came ready-set outside the artificial confines of 
the classroom.     
 

As mentioned earlier, the standard way to begin inquiring into a problem or issue is to see what 
needs to be asked about in order to deal with it. Such questions are probes into a problem domain. 
Raising questions and getting them into good order is therefore part of establishing an agenda for 
discussion in the classroom.  
 

Questions demand answers, but not in the way that questions asked by teachers normally do. 
For one thing, the answers must be searched for among the possibilities that present themselves. This 
means that students’ beginning attempts to answer the questions that frame their inquiries should be 
viewed as suggestions, rather than as providing the answer. Suggestions can take many forms, such as 
floating an idea, voicing an opinion, making a proposal, or forming a hypothesis.  
  

We may come to suggestions right off the bat or after having surveyed the ground, noting things 
that may help us in our quest. Even when we proceed directly from a question to a suggestion, there 
will be reasons in the background. Students who make a direct move of this kind can expect to be 
asked to provide reasons to back up what they say. In other words, it is assumed that the student has 
already latched onto some facts or features of the case and has those in mind when making the 
suggestion.   
 

This brings us to the complex business of reasoning and analysis. These activities ultimately aim 
to evaluate suggestions by analyzing ideas, scrutinizing assumptions, drawing out implications, raising 
counterexamples, and bringing fresh evidence to bear. Most of the tools of philosophical inquiry come 
into play here. Reasoning involves both inference-making and the assembly and evaluation of 
argument. Analysis encompasses a whole host of operations from classifying, distinction-making and 
defining, through comparing and contrasting, to exploring the criteria that govern the application of 
complex concepts.  
 

The complexity involved in exploring and evaluating suggestions is also partly due to the fact 
that it is not usually a single step-wise sequence. It is likely to track backwards and forwards as 
suggestions encounter difficulties and other suggestions are made, or we deliberate over the merits of 
competing points of view. There can also be inquiries within inquiries, adding further to the 
complexity. Even so, like fractals, they replicate the same process.  
 



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The outcome of classroom philosophical inquiry may take many forms. Having weighed 
competing suggestions, we may have come to a decisive judgment. Alternatively, there might be no 
agreed conclusion, but merely progress toward one. It may be that the issue is better understood, or 
simply a realization that we don’t know something we thought we did. Socratic discovery of ignorance 
can be the beginning of wisdom. 
   

Although both critical and creative thinking recur throughout such an investigation, we may 
consider the first phase up to and including the making of suggestions as predominantly creative, 
while the second phase, which involves reaching conclusions through the process of reasoning and 
analysis, is decidedly critical. Thus, successful stimulus materials are likely to engage the imagination 
and provoke thoughts and feelings that awake us to issues and problems and begin to raise questions 
in our minds. These things are more creative than critical in mood, and that continues on when 
suggestions spring to mind, or we brainstorm ideas. By contrast, reasoning as to the logical 
implications of a statement, bringing evidence in support of a suggestion, or presenting a 
counterexample to a claim, are critical in mood, as are such things as categorization, distinction-
making, definition, and analytical comparison.  
 

I do not mean to overplay this division of inquiry into critical and creative phases. In 
philosophy, very little critical thinking occurs without at least a modicum of creative thinking, and vice 
versa, with much of the work bearing a critical face on one side and a creative one on the other. The 
articulation of some idea requires the critical choice of vocabulary, for instance, and quite possibly 
self-correction in the process. While creative in tenor, the act involves critical oversight. Similarly, even 
something as obviously critical as mounting an argument against a claim involves the construction of 
an argument, which is an act of creation.     
 
Developing the Tools of Thought in the Classroom 
 

In what follows, I will attempt to flesh out aspects of the scheme presented in the previous 
section, restricting myself to the topics of questions and questioning, reasoning, and conceptual 
exploration. While much could be said about the means to be employed in other phases of inquiry, 
homing in on these three areas will allow me to concentrate on the most essential tools of thought 
that students will acquire.  
 
Questions and Questioning 
 

Let us begin with questions into a problem or issue that form the agenda for discussion. Our 
word problem has its roots in the Greek term πρόβλημα, formed from πρό (before) and βά̆λλω (throw), 
the meaning of the whole being that a problem throws something before you. It forms a hindrance or 
an obstacle to be cleared away. Of particular interest is the fact that in Aristotle’s logic a problem takes 
the form of a question as to whether a statement is true. That is, a problem throws a question before 
you as to the truth or otherwise of a given statement. We might say that the statement is problematic 
in the sense of being questionable. Let us, then, regard a problem as throwing questions before us that 
we must try to answer if we are to address the problem aright.  

 



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Earlier I made some remarks on the character of philosophical questions, but let me come at 
them again from the perspective of the classroom. First, philosophical questions ask about things that 
matter to us, but to which we do not have settled answers. That must apply in the classroom, if we are 
to motivate inquiry. In this respect, they stand in contrast to all those teacher’s questions that 
presuppose their answers and to which students are all too often unresponsive. Secondly, they invite a 
search for answers and are therefore open to various responses. This encourages creative and divergent 
thinking and consideration of different points of view in the classroom, which is enhanced by the fact 
that the inquiry is collaborative. Thirdly, we are looking at the kinds of questions for which the tools 
of philosophy are designed—questions whose possible answers compete for justification by appeal to 
reasoning and analysis. In the classroom, therefore, they provide a golden opportunity for students to 
learn to analyze ideas and reason well. 
 

It should not be assumed that students will be able to construct such questions without training. 
Interventions are needed. For example, it can be extremely helpful for students to learn to distinguish 
between questions according to their response demands. This can involve seeing that one question 
demands discussion, while another would be better addressed by consulting a reliable source, or that 
it will need some admixture of the two. Sometimes it will be to recognize that whatever answer you 
give to the question is really a matter of personal preference and that arguing about the matter is 
inappropriate or in vain. In the instances of special interest to us, it is a matter of seeing that no 
answer will suffice without the support of a carefully reasoned case. Learning to be a good questioner 
is largely a matter of learning by doing, but carefully targeted exercises and activities can set students 
on their way.4  
 

This brings us to the kinds of questions that are directly connected with the use of a whole raft 
of philosophical tools. So far, we have been looking at the questions that form the agenda of an 
inquiry. A great deal of questioning also arises throughout an inquiry. Since inquiry is by nature a 
form of questioning, this is hardly surprising. Typical questions in the classroom include ones like the 
following: What are you saying? Why do you think so? What’s supposed to follow from that? What 
sort of thing is that? Why isn’t it the same? These questions ask us to use the tools at our disposal to 
think about what is being said, by clarifying, giving reasons, and inferring, classifying, and making 
distinctions, in the cases just given. 
 

While the subject matter of philosophy is intrinsically of value in a child’s education, we are 
looking at it here through the lens of cognitive development. By constantly inviting such questions, 
philosophical discussion is an ideal vehicle for the development of critical and creative thinking. So 
long as the teacher is able to guide students to make appropriate moves in their thinking by asking 
such questions, and encouraging students to ask and address them, as discussion proceeds, I can think 
of no better means to that end. 
 

It is not possible in such a brief survey as this to give a detailed account of all the tools in the 
philosopher’s kit. As indicated earlier, I have chosen to concentrate on elementary tools used for 
                                                 
4 See my Philosophical Inquiry, Chapter 2, for a detailed discussion of questioning and exercises and activities to support its 
development. On response demands, in particular, see pp. 17-20, 43-4, as well as use of the Question Quadrant, pp. 20-23, 
45-7.  



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questioning, conceptual exploration and reasoning. As we move on from discussing questions and 
questioning, however, I would like to say something about why-questions and reason-giving. It is so 
basic to philosophical discussion in the classroom that it is worth singling out.  
 

Why-questions call for a reason and the giving and examination of reasons is an essential part of 
the inquiry process. Some why-questions seek an explanation, while others ask for a justification. The 
former questions are emblematic of scientific inquiry, as the latter are of philosophy. Even then, we 
need to distinguish between different kinds of justification. Sometimes we seek justification for some 
action or societal state of affairs, which we may call social justification, while on other occasions we seek 
reasons to justify some statement or claim, which is logical justification. Why-questions of logical 
justification are the ones of particular interest here. To attempt to justify a statement or contention is 
to reason about it, and reasoning about propositions is the bread-and-butter of philosophical inquiry.  
 
Reasoning 
 

Let us begin by thinking about reasoning in terms of its basic operations. Just as addition and 
subtraction are the basic operations of arithmetic, logical justification and inference are the basic 
operations of reasoning. Here is an example: 

Justification: It isn’t fair to give some people more opportunities than others because fairness involves 
everyone having the same opportunities.  

Inference: Fairness involves everyone having the same opportunities.  Therefore, it isn’t fair to give 
some people more opportunities than others.  

I have italicized the words ‘because’ and ‘therefore’ to mark these operations.5 Let us look a little 
more closely at what they involve, beginning with logical justification. In terms of language use, it 
involves logical relations between statements, where one or more statements are used to support 
another statement. From a cognitive point of view, it involves a relationship between judgments, where 
one or more judgments is used to justify another. I say this in order to point out that engaging 
students in logical justification shifts their attention from the relations between the things they are 
talking about to include the relations between their judgments and between the statements that they 
make. In so doing, it draws attention to their thinking. 

Similar remarks apply to inference. Inferences involve logical relations between statements, 
where one statement, the conclusion, is said to follow from one or more other statements, which are 
its premises. In terms of cognition, an inference involves a judgment that, in accepting the premises, 
we should accept the conclusion. We may grant the inference without assenting to the premises, of 
course, but when we judge the premises to be true, we have what is called an argument from the 
premises to the conclusion. As with logical justification, inference-making and argument represent a 

                                                 
5 I recommend sticking to these two words in the beginning stages of paying attention to reasoning. Some teachers of 
young children prefer to use the word ‘so’ instead of ‘therefore’ to introduce inference-making, but ‘so’ has so many other 
uses—isn’t that so? We might not use terms like ‘justification’ and ‘inference’ with young children, but we need to clearly 
distinguish between these operations. Instructions such as ‘Give a reason’ and ‘Draw a conclusion’ will do just fine in 
combination with ‘because’ and ‘therefore’. 



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shift from unselfconsciously thinking about our subject matter, to include awareness of the operations 
used in thinking about it. To use a word that has become fashionable in education, the shift is 
metacognitive.   

The import of this becomes clear if we extend the comparison with arithmetic. Children add on 
things and take them away long before they learn to enumerate. Coming to think about such actions 
in arithmetic terms involves a metacognitive shift in which the basic operations of addition and 
subtraction are consciously applied to them. The utility of this arithmetic overlay is obvious and we 
make early and thoroughgoing efforts to ensure that children become numerate. Children also move 
from judgment to judgment and one statement to another without thinking about the logical 
relations between them, and educational intervention is necessary to establish proficiency in 
justification and inference. While the value of logical literacy is no less obvious than in regard to 
numeracy, it is an educational scandal that our efforts have not been commensurate.  

Let me make two more points about the comparison with basic numeric operations. First, as 
Piaget long ago pointed out, such operations are reversible (Piaget, 1970). Numerical addition has its 
reverse in numerical subtraction. We can add 4 to 5 to get 9, for example, and subtract 4 from 9 to 
return to 5. Similarly, with logical operations. X because Y, has its reverse in Y, therefore X. You simply 
change the logical operator from ‘because’ to ‘therefore’ and reverse the order of the statements.6   

Secondly, elementary numeric operations exist within the systems of operations that characterize 
mathematics. Logic is no different. Its operations belong within systems, from elementary operations 
of justification and inference like those illustrated here, to propositional calculus, syllogistic logic and 
other forms of predicate calculus, the logic of relations, and so on, generally encountered only at the 
tertiary level. The same is true of mathematics, of course, with the difference being that students 
encounter a good deal of mathematics at the primary and secondary level, but seldom much logic—and 
it shows!   

Justification and inference assume significantly different forms and take on different roles in 
inquiry. In its traditional deductive form, reasoning is a truth-preserving operation. The standard way 
of expressing this is to say that valid deductive reasoning logically guarantees the truth of the 
conclusion given the truth of its premises. It is logically impossible for the premises to be true and the 
conclusion false. Deductive operations guarantee their results provided that you don’t make mistakes, 
just as you’re guaranteed to get the right result in arithmetic if you don’t make mistakes. 

While we make use of deduction within philosophical inquiry, it is less clear that it is deductive 
in its overall logical form. One possible argument runs as follows: According to Karl Popper (Popper, 
2002), scientific inquiry takes the form of hypothesis and test. To be testable, a scientific hypothesis 
must be falsifiable, in that, if certain conditions C fail to be met, then the hypothesis H can be shown 
to be false by deductive reasoning. Crudely put, the reasoning is this: If H then C. But not C. 
Therefore, not H. Alternatively, if H survives the test, it lives to fight another day. Philosophy is not 
science, of course, but it might be argued that the same logic should apply to it, if it is to deal with 

                                                 
6 By the way, while secondary students are familiar with . ˙ . as the shorthand for ‘therefore’, they are unlikely to know that 
˙ . ˙ is the shorthand for ‘because’. That makes one symbol the inverse of the other. The folks who devised that 
arrangement knew what they were doing!   



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substantive matters.   
 

This way of looking at inquiry places the formation and choice of hypotheses outside its logical 
framework. Before agreeing to do that, however, we need to consider how hypotheses are formed and 
chosen for further consideration. This is bound to be mixed, but let’s consider detective work, for the 
sake of argument. Observation of a crime scene and the questioning of witnesses may provide clues as 
to suspects worthy of investigation. Here, various pieces of evidence combine to form, not a proof, but 
a circumstantial case as to the identity of a culprit. The inference from the evidence to the suggestion 
that S is the culprit is strong enough to be worth following up, but is no logical certainty. The 
inference is what we call an inductive one.7  
 

Guided by this, we might say that inquiry has both inductive and deductive phases.8 Although I 
cannot argue the case further here, let us apply this pattern to philosophical inquiry in its most 
generalized form. It is important to note that this overall framework is consistent with the occurrence 
of both inductive and deductive reasoning moves at various points within it. The deductive move 
already mentioned in relation to Popper is known as modus tollens, but it is only one move among 
many within the systems of elementary logic that may occur. Nor should we overlook the use of 
deductive reasoning in employing special purpose devices such as counterexamples, and necessary and 
sufficient conditions.  
 

In regard to inductive operations, consider arguments from analogy. It might be argued, for 
example, that learning to think well involves the acquisition of skill, much as in learning a trade. So, 
just as you must learn to use the tools of a trade in order to be proficient in it, you need to learn how 
to use the tools of thought in order to think well. How is this argument meant to work? From the fact 
that the two cases are comparable in a significant respect (acquisition of skill), and that one has a 
certain further feature (mastery of the tools of the trade), it is inferred that the other will exhibit that 
feature as well (proficiency in the use of thinking tools). The argument is suggestive, but the fact that 
they share one feature does not prove that they share the other. If they do so, it is not out of logical 
necessity. Such an argument clearly involves an inductive inference.9  
 

Again, consider thought experiments. They are an argumentative device that asks us to imagine 
a scenario or situation and draw a conclusion from it. A favorite of mine comes from John Locke in 
his discussion of personal identity. Locke asks us to imagine that the soul of a prince has come to 
inhabit the body of a cobbler, whose own soul has just departed. Do we now have the prince or the 
cobbler? Locke is betting that you will choose the prince and then draw his conclusion.10 I particularly 
                                                 
7 Further inquiries into the hypothesis regarding S may well take the deductive form indicated above. It may be that, were S 
to be the culprit, then C must be the case. If further inquiries show that C is not the case, then S is removed from the list 
of suspects.        
8 For this view of the logic of inquiry, see Dewey (1991), esp. pp. 81-2. For an extensive and more complex treatment of the 
matter, see Dewey (1938), Chapter XXI.  
9 Under one way of analyzing the argument, it also includes a deductive step. For an introductory account of the analysis of 
arguments from analogy, see my Philosophical Inquiry (2020), pp. 124-5.  
10 See John Locke, An Essay Concerning Human Understanding, Chapter 27, § 15. This thought experiment is not actually a 
stand-alone argument in Locke. He employs it to forward an argument for distinguishing, as he puts it, the same man from 
the same person.  



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like this example because it reminds me of the fairy-tale of the frog prince, where it is a good bet that 
the young readers will side with Locke. There is no hint of deduction here.  
 

I haven’t the space to say more about reasoning, but we already have a decent list of reasoning 
operations and devices for use in the classroom: the basic operations of logical justification and 
inference, deductive reasoning, inductive reasoning, counterexamples, necessary and sufficient 
conditions, argument from analogy, and thought experiments. If students can acquire even a basic 
proficiency with them, they will have gone a long way to fulfilling the promise of philosophy in 
schools to raise the bar on reasoning in school education.11 
 
Conceptual Exploration 
 

As we did with reasoning, let us tease out the relevant operations. They may be divided into the 
categorical and the comparative. Categorical operations include such things as classification and 
division, conceptual opposition, categorical distinction-making, definition, and the construction of 
metaphor. Comparative operations include making comparisons of quality and comparisons of 
quantity, ordination, making comparative distinctions, and drawing analogies.12  

Let’s begin with classification and division. To classify something is to assign it to a class. Thus, 
to say that Cinderella is a young woman is to assign her to the class of young women. She is also a 
fairy-tale character, of course, which places her in an entirely different class, along with the Big Bad 
Wolf and Rumpelstiltskin. Likewise, to say that consciousness is a state of the brain represents a 
dramatic shift in classification from the traditional view that it is a state of the soul.  

Division involves dividing things of some kind into various sub-kinds, as in dividing cutlery into 
knives, forks and spoons, or dividing the mind into its various faculties. Similarly, we may divide 
ethical theories according to whether they are based on actions or based on virtue.  

Both division and classification generally admit of hierarchies of classes. Thus, we may further 
divide the class of spoons into, say, tablespoons, dessert spoons and teaspoons, just as we may divide 
action-based ethical theories into those that are teleological and those that are deontological.  

Once again, the comparison with addition and subtraction is instructive. Grouping things 
together and separating them form a pair of operations much like adding them on and taking them 
away. When formalized, the latter actions become basic numeric operations, while the former become 
basic conceptual operations. The one is as indispensable in learning to think conceptually as the other 
is in learning to think mathematically. 
 

It is worth pointing out that classification and division also form a pair of reversible operations, 
like addition and subtraction, or logical justification and inference. We can divide spoons into their 

                                                 
11 For a more detailed account of these and other reasoning tools, together with associated exercises, see Philosophical 
Inquiry, Chapter 4. See also my Twenty Thinking Tools (2006).  
12 It is an interesting and significant fact that categorical conceptual operations are related to deductive reasoning, while 
comparative operations have connections with inductive reasoning. Unfortunately, we do not have the space to explore 
that here. For a more detailed account of conceptual operations and related exercises and activities for the classroom, see 
Philosophical Inquiry, Chapter 3.  



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various kinds, for instance, and then gather them all together again just as spoons; or divide and 
subdivide ethical theories into their various kinds and then classify them together again just as ethical 
theories. 
 

Students need to learn to apply these operations both separately and in combination. Take 
conceptual opposition for an example of elementary use. When we say that bad is the opposite of 
good, for example, we set up opposing categories. To say that to be kind is good, for instance, is to 
classify that conduct in the same way that we did for Cinderella. Metaphor is the same. John Locke 
says of the mind in its initial state: “Let us then suppose the mind to be, as we say, white paper, void 
of all characters, without any ideas”. Here the mind, in its original condition, is classified as a tabula 
rasa.13    
 

For combination, consider distinction-making. Categorical distinctions involve a combination of 
classification and division. It is easy to overlook the combination because distinction-making 
concentrates on differences, and therefore on division. Still, to draw a distinction is to make a division 
between things in some category, and it is best to be clear about this by first classifying the things that 
we are going to divide. An obvious way of distinguishing between daggers and swords, for instance, is 
to say that the former has a short blade, whereas the latter has a long one. More fully, however, a 
dagger is a short double-bladed weapon, whereas a sword is a long double-bladed weapon. That is to say, 
they both belong to the category of double-bladed weapons (classification), which differ in being either 
long- or short-bladed (division). 
 

Distinction-making illustrates the fact that classification and division are the building blocks of 
other categorical operations. Definition follows suit. We might define a dagger as a short double-
bladed weapon, and in doing so we cite the category to which it belongs (double-bladed weapon) 
together with the feature that divides it from other things of that kind (being a short one). All 
categorical operations involve classification, division, or some combination of the two.  
 

Let’s now briefly consider comparative operations. In their most basic form, they deal with 
differences of degree with regard to some characteristic of the things being compared. Comparisons of 
quality provide obvious examples. If one person is said to be more reliable than another, for instance, 
then they are being compared in the degree to which they possess a certain quality: reliability. 
Comparisons of quantity are also like this, as when we say that Michelle has let us down less often 
than Danny, or that swords were used more frequently than daggers in medieval battles.  

  
Comparisons generally involve two-way relations. Consider more and less in the examples just 

given. If Michelle has let us down less often than Danny, then Danny has let us down more often than 
Michelle. If swords were used more frequently than daggers, then daggers were used less frequently. 
Similarly, if one performance is better than another, then the other is worse; if one course of action 
promotes happiness to a greater extent than other alternatives, then those alternatives promote it to a 

                                                 
13 An Essay Concerning Human Understanding, Book II, Chapter 1, § 2. If it had been said that we should conceive of the 
mind as like white paper, we would have had an analogy, of course, which is conceptually comparative rather than 
categorical.   



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lesser extent.  
 

These basic conceptual operations lend themselves to iteration. Consider ordination. Students 
vary in mathematical performance, for example, and it would not be at all difficult for their teacher to 
place a selection of them in order in terms of how well they do. Thus, student B’s performance is 
better than A’s, C’s better than B’s, D’s better than C’s, and so on. So far, that’s just variation in the 
quality of their performance, but it is the kind of thing that we can easily quantify, as indeed we do. 
You need look no further than their end of year marks in mathematics.  
 

Numerical comparison is as common in science as is the comparison of qualities and non-
numerical quantification in the arts and humanities. It should therefore come as no surprise that 
comparative operations in philosophy are overwhelmingly qualitative, and seldom mathematical when 
quantitative. One example will serve. When, in the field of ethics, a philosopher thinks about what 
makes an action right, it is almost certain to be a question of what properties or qualities an action 
should have for the concept of right to apply to it. John Stuart Mill, for instance, says that an action is 
right insofar as it maximizes utility, which he conceives of as happiness. That is to say, the action 
should have the attribute of promoting happiness, and do so to a greater extent than any alternative.14 
Quality and non-numerical quantity are combined in this conception. This example is particularly to 
the point about the difference between the humanities and science, because Mill is following Jeremy 
Bentham, who attempted to give utility a mathematical treatment with the utile as its unit. In doing 
so, he tried to convert a philosophical conception into one fit for social science.  
 

While some distinctions are conceptually categorical, as we saw, others are comparative. For 
instance, we might explain to a young child that tortoises and turtles are different from one another 
by saying that one is far smaller than the other. Here the distinction is obviously comparative. We 
might have said that one is little while the other is big, of course, which would have been categorical. I 
mention this because we often face a choice between a categorical and a comparative way of 
conceptualizing things, if only we realize it, and it can sometimes matter which choice we make. That’s 
one reason among many for attending to conceptual literacy.  
 

Like metaphors, analogies can be captivating. It is common for people to be struck by an 
analogy, which goes on to guide their thinking, even though its basis is unexamined. We are more 
inclined to scrutinize an analogy when it seems somehow inapposite. When it comes to conceptual 
exploration, however, a focus on the basis of comparisons is an aid to both critical and creative 
thinking. The ability to analyze an analogy, and say what makes it work or not, is a critical thinking 
skill, both in the study of literature and more generally; and sensitivity to the basis of comparisons is a 
source of creative thinking when it comes to students making figurative use of language.  
 

                                                 
14 While ‘greatest’ is a superlative, talk about the greatest happiness it is still a comparative conceptualization. The action 
producing the greatest happiness is the one that produces greater happiness than all those actions with which it may be 
compared.      
 
 



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One final point. It would be a mistake to leave you with the impression that conceptual 
exploration involves nothing more than the simple application of categorical and comparative 
operations. As a remedy, let me say a word about complex concepts. I have in mind concepts like 
friendship, fairness and freedom. The criteria that govern the application of these concepts tend to vary 
from one case to another, the cases being related by nothing more than what the 20th-century 
philosopher Ludwig Wittgenstein called a family resemblance. In other words, they are not defined by a 
common set of criteria. Some cases may be quite analogous to others, but others far less so, and their 
differences may be more of interest than what they have in common. This complexity means that the 
application of the concept is often contestable. We are all familiar with uncertainty and even open 
disagreement on occasion as to whether someone is truly a friend, some outcome is fair, or what it 
means to be free. The same applies to most of the concepts with which philosophy deals.   

 
Concluding Remarks 

 
Questioning, reasoning, and conceptual exploration, are hardly exclusive to philosophy, but the 

kind of questions with which it deals, its careful attention to reasoning, and the fact that conceptual 
exploration is central rather than ancillary to its efforts, means that philosophy combines all the basic 
ingredients needed for teaching students to think well in ordinary language in a way that marks it out 
from other disciplines.  
 

It is as well to acknowledge that philosophers and philosophical traditions differ in the emphasis 
that they place on one or other of the things we have been examining. For instance, some see 
philosophical inquiry as concerned primarily with establishing the truth about the things into which it 
inquires. Others see it as more concerned with the development of ideas that help to give meaning to 
our existence. These differences obviously make a difference to the kind of discourse in which they 
engage. Those who regard philosophy as a quest for meaning are likely to emphasize conceptual 
exploration, while those dedicated to the pursuit of truth are more likely to expend their efforts on 
reasoning. Still, regardless of its emphasis and variety, philosophical inquiry remains an amalgam of 
the ingredients presented here.   
 

This completes our survey of philosophical discussion in the classroom. I am all too well aware 
that I have touched only lightly on features of the terrain that deserve far more detailed treatment 
than space allows here. Let me use the opportunity, then, to encourage you to follow these matters up, 
either in the works to which I have referred, or those of your own choosing. Provided you do so with 
an eye to converting what you find into classroom practice, your efforts will be richly rewarded.     
 
References 
 
Cam, P. (2006). Twenty Thinking Tools: Collaborative Inquiry for the Classroom. Melbourne: Australian 
    Council for Educational Research. 
Cam, P. (2020). Philosophical Inquiry: Combining the Tools of Philosophy with Inquiry-based Teaching and 

Learning. Lanham, MD: Rowman & Littlefield. 
Dewey, J. (1938). Logic: The Theory of Inquiry. New York: Henry Holt and Company. 
Dewey, J. (1991). How We Think. Buffalo, NY: Prometheus Books. 



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Dewey, J. (2004). Some stages of logical thought. In Essays in Experimental Logic. Mineola, NY: Dover 
Publications. 

Piaget, J. (1970). Genetic Epistemology. New York: Columbia University Press. 
Plato, Theaetetus 190a. https://www.gutenberg.org/files/1726/1726-h/1726-h.htm 
Popper, K. (2002). The Logic of Scientific Discovery.  London: Routledge. 
Vygotsky, L. S. (1978). Mind in Society: The Development of Higher Psychological Processes. Cambridge, 

Mass: Harvard University Press.   
 
Address Correspondences to:  
Philp Cam, 
School of Humanities and Languages, 
University of New South Wales. 
Sydney, Australia 
Email: p.cam@unsw.edu.au 

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