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Teaching Philosophy

Teaching Argument Evaluation in An Introductory Philosophy Course

Jonathan Lavery & Jeff Mitscherling
University of Guelph, Ontario
jlavery@uoguelph.ca, jmitsche@uoguelph.ca

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ABSTRACT: One of the greatest challenges in teaching an introductory philosophy course is convincing students that there are, indeed, reliable standards for the evaluation of arguments. Too often introductory students criticize an argument simply by contesting the truth of one of its claims. And far too often, the only claim in an argument that meets serious objections is its conclusion. For many students, the idea that an argument displays a structure which can be evaluated on its own terms is not very difficult to grasp. Unfortunately, the idea is grasped only in an abstract way, with insufficient appreciation of how structural problems manifest themselves in concrete arguments, and without the vocabulary for formulating structural criticisms. But this paper is not simply about teaching logic, it is about pedagogy. Our task is to instill in the student the habit of clear thinking. When we send our students out into the world, we have to ensure that they are prepared for it.

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One of the greatest challenges in teaching an introductory philosophy course is convincing students that there are, indeed, reliable standards for the evaluation of arguments. Too often introductory students criticise an argument simply by contesting the truth of one of its claims. And far too often the only claim in an argument that meets serious objections is its conclusion. For many students, the idea that an argument displays a structure which can be evaluated on its own terms is not very difficult to grasp; unfortunately, the idea is grasped only in an abstract way, with insufficient appreciation of how structural problems manifest themselves in concrete arguments, and without the vocabulary for formulating structural criticisms.

But this paper is not simply about teaching logic — it's about pedagogy. The introductory philosophy student's inability to recognize argument structure presents us with a problem that cannot be addressed simply by "teaching logic." The problem that confronts us addresses a fundamental pedagogical concern: Our task is to instill in the student the habit of clear thinking. When we send our students out into the world, we have to make sure that they're prepared for it. This is not simply a matter of providing them with "tools." We've looked at logic that way — and we've approached teaching logic that way — for far too long. Certainly logic may be employed as a tool; it can serve as an incredibly powerful tool, as we who teach it know full well. But it's not logic per se that we should be concerned with in our introductory courses. We want to teach our students how to think clearly and responsibly. There is certainly a moral edge to this view of the situation, and the manner in which we approach our pedagogical concern will not be without further philosophical prejudice. Ours is Aristotelian. We have found that giving our students the basics of term logic serves our purpose well. We do not introduce it as a tool for argument analysis — a strong case can easily be made for the superiority of truth-functional logic in that respect — we present it, rather, in the way that a kindergarten teacher brings toys into the classroom. And we make it clear that term logic has limitations — it's not an all-purpose tool. But again, that's not the point. Teaching the basics of term logic pulls the students into a way of thinking that is ordered, directed, and clear. We do not deal with fallacies, for an obvious reason: If you're trying to instill a proper habit, you have to use a proper model. We should not be teaching our students how not to do things. If clear thinking is achieved, fallacious reasoning will be recognizable. Instead of beginning with criticism, we focus first on clarity. We also keep in touch with the content of the arguments: Term logic preserves the content of the arguments in a way that truth-functional logic can only envy, and students appreciate this contact with the real world.

We here present a bare-bones system of argument analysis and evaluation that successfully introduces beginning philosophy students to argumentation with a minimal investment of class time. The system is derived from Aristotle's term logic, and we shall be discussing the comparative merits of term logic and truth-functional logic for part of the presentation. First, however, let us state in a general way the special constraints and demands of teaching any system of logic in an introductory philosophy course.

1. It must be accessible to any first-year university student, and the less that needs to be presupposed the better.

2. It must be broad enough to apply to a wide variety of arguments.

3. It must encourage a systematic grasp of logical principles and concepts.

4. There must be an evaluative component.

5. Instruction must make efficient use of class time.

The Relative Merits of Term Logic and Truth-Functional Logic

Using the five points listed above, we shall explain why a logic of terms is desirable in the first place. Term logic does not recommend itself overwhelmingly on each of the five points, but on all five it is at least the equal to sentential logic. Moreover, the points on which it may be more strongly recommended are crucial.

(1) We grant that truth-functional, sentential logic without the apparatus of predicate notation should be accessible to first-year students. The rules of bracketing and the system of notation needed for sentential logic should not present special difficulties for any university students. Moreover, since the sentences themselves are left unanalyzed, inferences can be represented rather intuitively. Term logic, on the other hand, requires students to analyze sentences, but the subject-predicate syntax required for this analysis should be familiar. Additionally, the method of notation and representation needed for the system we want to present does not require using any special symbols. The most difficult new vocabulary that students encounter in our system is "distribution," and it is our experience that the difficulties students have when this concept is introduced resolve themselves after they get a little practice at translating English sentences into proper categorical form. In terms of accessibility, our system is probably the equal to truth-functional logic.

(2) Again, in terms of breadth, the two systems are comparable. Each has its limitations, but this is inevitable given the specialized needs of studying logic as only one part of the term's work — and in terms of class time, only a small part. All the same, term logic has surprising breadth when it is adapted to accommodate enthymemes and chain syllogisms, and the system outlined below is adapted to do precisely that.

(3) & (4) It is in its potential for depth and evaluative power that a system of term logic may be recommended over sentential logic. These two considerations (depth and evaluative power), while distinct, are not separable. It is precisely because our system of term logic has such a strong evaluative component that it is able to convey some of the deeper, more difficult concepts of argumentation. Almost from the start, students must make use of such evaluative standards as truth, validity and soundness; it is also possible to incorporate other evaluative notions, such as relevance, consistency, sufficiency, and inference. And all of these notions can be introduced, and successfully grasped by the student, in a quite brief presentation. We'll be returning in what follows to the discussion of the depth and evaluative power of term logic.

Sentential logic has pedagogical limitations in an introductory course that can be explained succinctly. If the class studies only the inference rules and leaves out truth-tables, two limitations immediately arise. First, there is no evaluative component, and secondly, students who only derive proofs are likely to get the impression that all deductive arguments can be made valid — one need only fill in the implied steps between the stated premises and the stated conclusion. Yet in order for a class to study both the inference rules and the truth-tables, a great deal of the class time has to be given over to technical matters, so this strategy has simply to abandon the demand of point 5, that the logic unit of an introductory course be covered efficiently. (We'll ignore the possibility that a class might study truth-tables without studying inference rules.)

(5) We have already expressed doubts concerning the ability of sentential logic to convey the normative dimension of logic in a sufficiently brief period of time. This point is worth stressing: It is important that a logic unit in an introductory course be no longer than is necessary. For two chief reasons, an introductory philosophy course is not the place to examine issues in the philosophy of logic. First, even a superficial treatment of such issues must demand far more time and attention than can be devoted to them as components of merely one part of one course. And second, the excitement of philosophy, for the overwhelming majority of students in any general introductory philosophy course, will always be found in the liveliness and diversity of its issues. The logic component of a course should supplement and foster, not replace, this feature of the course. Furthermore, if logic is introduced properly, students are less likely to get the impression that the arguments offered in response to these issues and problems are verbal trickery. Even if the structure of a particular argument — say, for example, the argument from design — doesn't lend itself to analysis in terms of the system of logic that they have studied, students with some background in logic will at least recognize that there must be some kind of logical structure underlying the argument. The system we outline below is designed to instill an appreciation of the fact that all arguments have some kind of structural component, and that this structural component may be assessed apart from the argument's content.

The Simpler, The Better

For three reasons, we do not use Venn diagrams. First, they give students a technique for evaluating arguments, but they give no indication of what rule of validity is violated in an invalid argument; the students know that the argument is invalid, but they don't know why. Second, the diagrams become unworkable with enthymemes and chain arguments; you'd need a blackboard the size of Kansas. And third, students inevitably find some of the diagramming rules unintuitive — particularly those having to do with the placement of x's. So our first decision was not to use Venn diagrams. Our second decision was not to introduce the terminology of figures and moods; with the basic logical thinking that we're trying to teach, this only adds technical details while providing no obvious benefits. And third, we decided that the logic unit focus entirely on intermediate inferences, leaving aside immediate inferences (along with the square of opposition). What remains after these modifications is a deductive system for the analysis and evaluation of intermediate inferences in terms of distribution and negation rules. Without formally studying the principles of immediate inference, students may not be able to translate very sophisticated arguments, but consideration of such arguments is best postponed anyway. Again, we're speaking of a general introductory philosophy course, not a course devoted exclusively to logic or critical thinking. With this always in mind, the instructor must carefully formulate each exercise so that it makes its point clearly and without unnecessary confusion. Not being held in check by translation difficulties, students are able to move quickly to the evaluation of enthymemes and chain arguments, which is where the normative power of logic can be most impressive.

The system is introduced in the following order:

(1) Translation of declarative sentences from English into proper categorical propositions.

(2) Identification of the different parts of syllogisms.

(3) Evaluation of categorical syllogisms for validity and soundness.

(4) Reformulation of arguments.

(5) Evaluation of enthymemes for validity and soundness.

(6) Evaluation of chain syllogisms for validity and soundness.

With judicious use of class time, all of this material can be covered in six hours. Some instructors may prefer to study logic as a self-contained unit (either early in the semester or several weeks into it); others may prefer to study the logic one hour per week over the course of six weeks. (In the next section of the presentation, we will assume that the logic unit consists of six one-hour classes, spread out over two weeks). Now we'll outline the system itself, and offer some strategic suggestions for its introduction. Then we can consider how the system may be supplemented with class discussion of implication, inductive logic, analogical arguments and informal fallacies.

Teaching A Unit of Term Logic

When teaching any subject in philosophy, it's necessary to get the students to think clearly on the matter at hand. This also assists them in discerning some of the deeper problems and puzzles in other matters. With logic, it's crucial that students get a clear presentation of the technical apparatus in order to see the deeper issues involved in the justification of inferences. In order to accomplish this, we recommend that translation difficulties be minimized as much as possible. This recommendation applies both to examples discussed in class and to arguments assigned as part of the student's take-home exercises. It is important that the answers for the student's take home exercises be readily available (on reserve, posted outside the office, circulated with the exercises, etc.) so that students develop some independence with the material and class time can be devoted to the introduction of new material.

Session 1

The first class distinguishes arguments from other forms of prose (exposition, analysis, narration, etc.). Premises and conclusions are introduced as the primary components of arguments, and they are explained in connection with coordinating conjunctions and conjunctive adverbs that function as logical connectors ("for," "since," "therefore," etc.). Declarative sentences are explained in terms of a familiar evaluative criterion: truth. Truth itself need not be explained in great detail (fortunately), but it should be stressed to students that, in arguments, the evaluative function of truth comes into play only in the assessment of premises. Finally, some of the technical apparatus of term logic can be introduced: the distinction between subject and predicate, the copula, quantification (all, some, none), and the four categorical propositional forms ("a," "e," "i" and "o"); the special problems of singular propositions, and interpretative strategies of the definite article and proper names should also be covered. At this point students should be able to translate English sentences into proper categorical propositions. For example: "Most basketball players are tall" becomes "Some S are P."

Note: This is the best time to rehearse the fundamentals of punctuation. We're all sufficiently familiar with the problem of students coming to us with inadequate knowledge of basic English grammar. Right here, at this point in the course, you can solve part of that problem by quickly reviewing the proper and improper uses of the period, comma, semicolon, colon, dash, and apostrophe. It's helpful to include something like Margot Northey's excellent little book, Making Sense, in your list of required texts for the course. You can refer the students to it right here. (If you have the time and interest, you might also here consider a digression on the philosophy of language, or philology or linguistics. As John Lyons writes (although not entirely accurately) in his Introduction to Theoretical Linguistics (Cambridge 1969, p.4): "Traditional grammar, like so many other of our academic traditions, goes back to Greece of the fifth century before Christ. For the Greeks 'grammar' was from the first a part of 'philosophy.' That is to say, it was part of their general inquiry into the nature of the world around them and of their own social institutions."

Assignment: A few pages of declarative sentences to be translated into categorical propositional form. Quantity is the key at this point. Give the students lots of simple sentences that pose no problem to translation. Then, of course, you make it harder. Your goal should be to push the categorical proposition as far as it can go.

Session 2

In this session you can build on the forms of the categorical proposition to introduce some of the more technical features of syllogistic arguments. Some features of the syllogism may be operationally defined using the subject/predicate analysis of declarative sentences: major and minor terms, major and minor premises, and the middle term. The most difficult concept of the unit will inevitably be distribution. This topic may be broached now, but the distribution rules for validity are best left until the next session, by which time students will hopefully have won some familiarity with the analysis of the syllogism. Distribution should definitely be introduced systematically, using the following chart:

Universal affirmative: (d) S a P (u)
Universal negative: (d) S e P (d) [commutative terms]
Particular affirmative: (u) S i P (u) [commutative terms]
Particular negative: (u) S o P (d)

Commutation need not be discussed at all, but it may be introduced as a way to speed the translation of universal negative and particular affirmative propositions. At this point, students should be able to identify all the parts of a syllogism.

Assignment: A series of arguments for translation into proper syllogistic form and analysis.

Session 3

In this session, by reference to the rules of validity, the students are introduced to some of the most fundamental concepts of reasoning: truth, validity, soundness, and distribution. The session should dwell for a while on an argument that is capable of bringing out the demonstrative and evaluative power of syllogistic reasoning. The following argument from Nabokov has proved especially useful as a means for introducing the rules of validity:

Other men die.

I am not another man.

Therefore, I will not die.

This argument may immediately look suspect to the students, but at this point they will still have difficulty pinpointing exactly where it goes wrong. And since its premises are true, they should be open to the suggestion that this argument suffers from a structural defect. So truth, the most familiar evaluative criterion they have so far encountered, will not be of service in the assessment of this syllogism. Leave the argument on the board, and promise to return to it after discussing validity in general and the rules of validity for syllogisms in particular.

The session should open with the distinction between truth and validity, and both concepts be explained as components of soundness, for the particular rules of validity for term logic will then provide the students with the conceptual tools with which to grasp these concepts. The Nabokov argument breaks down like this:

All M are P (d) M a P (u)

No S are M (d) S e M (d)

No S are P (d) S e P (d)

By intuition alone, the student will know that something's wrong with the argument but will not be able to identify what that thing is. But the rules of validity make it crystal clear: we have a fallacy of illicit major: P is distributed in the conclusion but not in the major premise. At this point, you can easily begin to clarify the notion of distribution. Referring to this example, you can point out that while not every member of the class defined by P ( i.e., "things that die") is being referred to in the major premise (in which P is therefore undistributed), in the conclusion, on the other hand, every member of the class defined by P is being referred to (and so P is distributed there). The discussion of distribution at this point seems in fact to sharpen the students' logical-intuitive abilities, and perhaps their healthy paranoia: the students, not wanting to walk into a trap, suddenly begin to slow down and focus more clearly on what is actually being stated in each individual proposition before proceeding to the next one.

Assignment: A series of arguments for translation into proper syllogistic form and evaluation.

Session 4

In this session the importance of clarity and conciseness is brought home to the student. Two syllogisms should be written on the blackboard as examples. The first syllogism should contain an obvious equivocation, and the second should be an enthymeme. The first example can be used to discuss one technical matter and two important concepts. The technical matter has to do with the number of terms employed in an argument: a syllogism must contain only three. The concepts are ambiguity and relevance. The discussion of relevance in the context of the first example leads naturally into how to supply the missing proposition in an enthymeme, your second example.

Assignment: A series of enthymemes.

Session 5

The analysis of lengthy passages containing syllogistic reasoning is effective in demonstrating the scope and power of logical evaluation. We outline a step-by-step procedure that gives students a means for analysing and evaluating passages that students can master without great effort. It is possible in one hour to demonstrate the procedure by analysing and evaluating two different chains, each of which consists of at least three linked syllogisms. The function of extended arguments can be explained in terms of sufficiency, a concept that the student can easily grasp by seeing how a proposition presented as belonging to one of the linked arguments may also be employed as a premise in another of the arguments.

Assignments: Several chain syllogisms.

Session 6

This session should be devoted to the examination of the limitations of term logic. It has proved useful to consider simple arguments that make use of very basic truth-functional logic (modus ponens, modus tollens, and the hypothetical syllogism are easily enough explained). While these can usually be translated without too much effort into the form of a categorical syllogism, the awkwardness of doing so is clearly prohibitive. At this point, however, the battle is already won. The students are actively engaged in the logical analysis and evaluation of arguments.

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