Teaching and Learning > DISCOURSE

Notes on Teaching Logic

Author: Peter Milne

Journal Title: Discourse

ISSN:

ISSN-L: 1741-4164

Volume: 4

Number: 1

Start page: 137

End page: 158

Return to vol. 4 no. 1 index page

p>These notes don't reach any conclusions. Their purpose is to point to issues one needs to think through seriously when thinking about logic teaching. They indicate some of the relevant literature where some of these issues are addressed, but they also raise points that seem to have been overlooked. They aim to promote informed discussion. That indeed was their origin: they are descended from an internal discussion document prepared a few years ago when the then Department of Philosophy at the University of Edinburgh was reviewing its logic teaching.

 

§1 Three views of the aim and purpose of logic teaching

1.1 The fundamental issue that must be resolved before questions of course content and teaching methods can be addressed is the aim and purpose of teaching logic. Closely tied to it are questions regarding the role of logic in philosophy and the nature of logic itself. There are, it seems to me, three overlapping views of the purpose of teaching logic: I'll call these the therapy, the toolkit, and the body-of-knowledge views. Summarising each:

1.2 Therapy

We teach students logic so that they become better able to recognize and to construct good arguments themselves in philosophy and other disciplines.

1.3 Toolkit (or organon if you prefer the classical allusion)

Formal logic is an indispensable tool (weapon) in the toolbox (arsenal) of every philosopher (or at least every analytic philosopher). The most obvious occasions when logic is used in this way occur when the formal language of first-order logic is invoked for the perspicuous representation and/or disambiguation of theses whose natural language expression is less than straightforward. The toolkit view suffers the disadvantage that it is paid lip-service but no more: in teaching philosophy we often fight shy of using logic outside philosophy of science and philosophy of language. Rarely is epistemic logic employed in teaching epistemology; even less frequently is deontic logic used in teaching moral philosophy.1 If the toolkit view is intended seriously then logic ought to be integrated into the teaching of other parts of philosophy, most obviously metaphysics and epistemology but also other areas. I know of only one example of a textbook that adopts this line: William Brenner's Logic and Philosophy: An Integrated Introduction.2

1.4 Body-of-knowledge

Much as in, say, an introductory course in moral philosophy there is a standard set of concepts, theories involving those concepts, forms of argument and ragbag of tricky cases that is played off against moral intuitions, and perhaps used to subject those intuitions to critical scrutiny and to refine them, so logic comprises a similar stock of concepts, theories, forms of argument, and tricky cases that is played off against intuitions about "what follows from what". This much logic has in common with, to stay with the example, moral philosophy on the body-of-knowledge view, but it also differs in that, like the sciences rather than other parts of philosophy, it aims at a systematic account of a body of "phenomena" on which there is good agreement; moreover it makes appeal to formal methods of representation (a feature of logic that goes back at least to Aristotle's schematic use of letters and the Stoics' of ordinal numbers) and formal techniques. Unlike the sciences, the standards of assessment are not by-and-large empirical; unlike mathematics, logical theories can be assessed critically much in the way moral theories are. (A defect of much logic teaching and many logic textbooks is to present the subject as cut-and-dried, ignoring the sometime fractious debates in logic—or in the philosophy of logic, if you prefer—that have occurred especially in the twentieth century. Many of these debates are not so recondite that the issues cannot profitably be raised in undergraduate and even first year teaching.)

1.5 I have devoted most space to the body-of-knowledge view as it tends to be overlooked in discussions of logic teaching. (For example, I discern no trace of it in Helen Beebee's 'Introductory Formal Logic: Why do we do it?'3.) The three views do overlap, especially the therapy and toolkit views, so that arguments both for and against aspects of logic teaching practice may presuppose elements of more than one of these perspectives.

§2 Logic and reasoning

2.1 Neither the therapy nor the toolkit view immediately suggests that the benefits of education in logic should be limited to philosophy. Indeed, one of the familiar defences of logic teaching is that it imparts a transferable skill, i.e. one which can be put to good use in other branches of philosophy and in other disciplines. What evidence is there that this is so? Precious little, as Alec Fisher observes:

Like many others I hoped that teaching logic would help my students to argue better and more logically. Like many others, I was disappointed. Students who were well able to master the techniques of logic seemed to find that these were of very little help in handling real arguments. The tools of classical logic ... just didn't seem to apply in any straightforward way to the reasoning which students had to read in courses other than logic.4

This experience is in line with the ideas of psychologists such as William James, Jean Piaget and Peter Wason, who have all denied that training in following systems of abstractly presented rules has any effect on everyday reasoning. Fisher has a ready explanation:

[I]f you look at almost any modern formal logic book you will be struck by the remoteness of its examples from the kind of reasoning anyone would actually use. [...] Not only are most of the examples discussed by modern logic remote from real reasoning, modern logic explicitly restricts attention to reasoning of very particular kinds. [...]
For modern formal logic, the object of study is mostly the kind of argument which can be displayed on the model of a mathematical proof, leading from premises to conclusion, aimed at a universal or no particular audience, and evaluated in terms of whether it 'establishes' its conclusion by generally objective standards and not at all in terms of whether it convinces the intended audience.5

Moreover, the model of mathematical proof in question belongs to what philosophers of science call the context of justification: it is an idealization of the sort of mathematical proof one finds in expositions of mathematical results or theories from Euclid on. It has little to tell us about how to find, construct and develop arguments and for just this reason has been held to do a disservice to mathematical education.6

What goes for mathematical education presumably goes doubly for philosophical education. Fisher urges that we philosophers leave formal logic to computer scientists and seek elsewhere for a general theory or science of reasoning.7

2.2 Fisher's conclusion is much too hasty, not least because it fails to take account of alternatives to the therapy and toolkit views of the purpose of logic teaching. It fails to distinguish between logic and a descriptive science of reasoning. It fails to do justice to the hard-won insight that, in Ramsey's phrase, logic is a normative science; logic, since Frege, has been clearly separated from psychology. Logic is "the ethics of belief";8 in Frege's terms it seeks "the laws of truth", not "the laws of thinking".9 This is not to say that formal logic has no connexion with ordinary reasoning. Of course it does, and the criteria formal logic uses for the evaluation of what it considers to be arguments are arrived at in the attempt to achieve reflective equilibrium between, on the one hand, intuitions about good inferential practices and the aims of deductive inference and, on the other, our systematic (and usually formal) theories of valid inference. (The theories involve both syntactic specification of rules of inference and criteria for the semantic evaluation of inferences.)

2.3 Given this view of the nature of logical inquiry, it would not be in the least surprising if the typical examples of reasoning considered in a first logic course are somewhat stilted and artificial: one aims first to obtain a viable theory that treats these cases adequately before tackling the full range and subtlety of argument in everyday usage.10

As in any scientific enterprise there are hazards in artificially isolating cases, but there are also rewards for by doing so one cuts down the range of phenomena to be dealt with initially to a manageable size. One then extends the resulting theory with the aim of progressively accommodating the diversity and complexity of actual cases. This is the case with logic too, where there are, e.g. modal, temporal, deontic and epistemic extensions of propositional and first-order logic which draw into the ambit of formal logic types of inference not amenable to standard logic.

The development of expert systems in artificial intelligence has spawned a vast amount of work attempting to model in greater detail everyday reasoning (or at least the better episodes in the everyday reasoning of experts). What is important here is that this work is much less a corrective to the logic familiar to philosophers than an extension of it: the methods and results of, primarily, firstorder logic are presupposed in the work of those who seek to systematize the very sorts of argumentation that Fisher claims are remote from those examined in the teaching of elementary logic.11 As Paul Krause and Dominic Clark say:

The irony is that the formal models of practical reasoning ... are more complex than classical logic; it is harder to grasp the intuitions that underlie them, and they are computationally intractable in the general case.12

2.4 It should perhaps be pointed out that none of the above shows that the techniques for the evaluation of arguments that are taught in formal logic cannot be applied to arguments encountered in philosophy and other disciplines. They can, sometimes with a great deal of success. Furthermore, even if the techniques cannot always be applied, this is not to say that the discipline instilled in the mastering of the techniques is not indirectly beneficial. This takes us back to a claim of Ryle's, who likened the learning of formal logic to the parade-ground drill of soldiers: the drills are not performed on the battlefield but it is because of the discipline instilled in drilling that the soldier can perform effectively on the battlefield. 13 So, is, then, the difference between the unnatural arguments of formal logic and the unnatural arguments of critical thinking one of kind, of degree, or is there no difference on this score?

2.5 Because most of the critical discussion of the teaching of formal logic has concentrated on its inapplicability to "real arguments", I have concentrated here on the application of formal logic to arguments. This disregards other uses of formal logic, such as the perspicuous representation of logico-grammatical form and the development of the semantics of perspicuously represented forms. Parallel to the debate on argument, move and counter-move can be made: formal logic deals with a narrow range of examples; divide and conquer; the semantics of more complex forms is not straightforward as, say, Russell's theory of descriptions and Davidson's analysis of the logical form of action sentences shows; the project of formal semantics in linguistics does not, by-and-large, correct but builds upon the results and methods of formal logic, and in any case issues in analyses more complex than those encountered in a first course in formal logic.14

§3 Critical thinking and informal logic

3.1 Especially in North America, the critical thinking and informal logic movement has gained much ground in the past thirty to thirty- five years. Many have converted to the movement for reasons similar to Fisher's: disappointment with the results of teaching formal logic and dissatisfaction with its perceived lack of application to ordinary reasoning. (Notice that the therapy view is often an implicit, if not explicit, presupposition of those who follow this route into the movement.) Further impetus was given by the revival of interest in rhetoric due in significant part to the work of Chaim Perelman.15 Fisher likens the present debate on logic teaching to a Kuhnian scientific revolution, critical thinking/informal logic being the new paradigm now competing against the old mathematics-based model. To his credit he notes that, as such, the movement is confused and exploratory.16 Some of the confusion is worth exploring further.

3.2 Critical thinking vs. informal logic

As is common practice I have written of the critical thinking and informal logic movement and for many authors the only distinction to be drawn is that, perhaps, critical thinking has a broader compass. For others there is not just difference but opposition. The basis of their claim is a distinction between, on the one hand, informal logic as a "logic of argumentation", especially practical, everyday argument, differing from formal logic in its use of non-formal methods in analysis and evaluation,17 and, on the other, critical thinking as a discipline often said to be closer to epistemology than logic, a sort of mental hygiene practised so as to encourage critical attitudes to arguments and their construction. Thus John McPeck has said that 'critical thinking can be described as the propensity and skill to engage in an activity with reflective scepticism';18 Mark Battersby has claimed that critical thinking concerns epistemological norms rather than rules of logic and has likened it to applied ethics.19 Trudy Govier, author of A Practical Study of Argument,20 one of the most highly regarded of the second generation of textbooks in the area, asserts that critical thinking ought to go beyond the analysis and criticism of arguments, both in the modes of evaluation it employs and in considering types of discourse other than arguments.21 Harvey Siegel maintains that an epistemology underlies critical thinking, the latter being concerned with the warrants for belief and the performance of actions on the basis of reasons.22 (Unexpectedly, one line of complaint some proponents of informal logic run against critical thinking is the latter's dependence on the methods of formal logic in evaluating arguments.23)

Informal logic textbooks often comprise little more than a dilution of formal logic, including elements of propositional logic and traditional syllogistic together with a strong emphasis on classifying fallacies under either traditional terms or the author's own—'The bread and butter of the informal logician is the fallacy'24—and so ignore rhetorical topics such as the persuasiveness of arguments. As Brennerobserves, a danger lurks:

It is better to forget all the fallacy labels learned ... than to develop an "uncritically critical" attitude in our use of them. For unless we get in the habit of carefully justifying our applications of fallacy labels, we may be adding to the sophistry in the world rather than combatting it.25

A further danger is that without some theoretical framework in which to place the activity of fallacy-spotting it can lead to an overemphasis on the particular at the expense of the general and a negative view of logic and reasoning as taught subjects.26 Leo Groarke and Christopher Tindale suggest that if criteria for constructing good arguments are to be taught more than the avoidance of fallacies must be invoked: the negative criteria testing for bad arguments that are provided by fallacies must be used as a basis on which to construct positive criteria for good arguments.27 Formal, rather than informal, logic may have a role to play here28 as may formal methods akin to those developed in formal logic. Douglas Walton, one of the most prolific authors in informal logic and argumentation theory, informs us that:

[The] new [informal] logic is, or should be, based on new theoretical foundations including abstract structures of formal dialogues and pragmatic structures of discourse analysis.29

The theoretical framework behind informal logic is likely to be more, not less, complex than formal logic.

3.3 Critical thinking vs. informal logic vs. argumentation theory

While some clearly do not see much difference between critical thinking, informal logic, and argumentation theory, for others the dispute over aims and methods can become a little heated. Thus on the one hand Gerhard Preyer and Dieter Mans, editors of a volume of ProtoSociology on reasoning and argumentation, say, 'Since the 70's there are broad researches on the theory of argumentation called "informal logic" and "critical thinking"', going on to clarify that they prefer the terms "analysis of arguments" and "theories of argumentation" over "informal logic" or "critical thinking" simply because the word "argumentation" points to the type of work we are doing.30

On the other hand, McPeck, champion of critical thinking, complained that textbooks in informal logic 'are too preoccupied with getting on with the business of naming and describing fallacies to devote much space to explaining precisely what informal logic is supposed to be'. Aware that proponents of neither would like the comparison, he likened informal logic to classical rhetoric.31

Later he was to continue the attack,

It is clear to [Harvey] Siegel, and to me, that the ILM [Informal Logic Movement], continues to proceed along a high-profile path without the slightest knowledge of the more serious literature in the philosophy of education.32

On why that's not the non sequitur it may appear to be, note Groarke's characterization of the Critical Thinking Movement 'which has as its goal the development of a model of education which places more emphasise on critical inquiry'.33 In the hands of some of its advocates, critical thinking aims at a restructuring of the whole practice of education at all levels.34

Writing in 1981, McPeck called 'correct' the opinion expressed by Ralph Johnson and Anthony Blair that 'there is not, at the moment, anything resembling an adequate theory of argument'.35 It is startling, two decades later, to find Frans van Eemeren, mainstay of the Amsterdam school of argumentation theorists, expressing in similarly trenchant manner, similar qualms about the lack of precision in the methods of informal logic:

Blair and Johnson have indicated what they have in mind when they speak of an informal logical alternative for the formal criterion of deductive validity. In their view, the premises of an argument have to meet three criteria: (1) relevance [to the conclusion], (2) sufficiency and (3) acceptability. These criteria are introduced in Johnson and Blair (1977 [= 'The Current State of Informal Logic and Critical Thinking']) and they are, sometimes under different names, adopted by other informal logicians ... . In the case of 'relevance' the question is whether there is an adequate (substantial) relation between the premises and the conclusion of an argument; in the case of 'sufficiency' the question is whether the premises provide enough evidence for the conclusion; in the case of 'acceptability' the question is whether the premises themselves are true, probable or in some other way trustworthy. None of the criteria has been more clearly defined. Informal logic is not yet a fully-fledged theory of argumentation.36

3.4 Critical thinking as a learnable skill

Probably the single most important controversy within the critical thinking and informal logic movement has concerned whether critical thinking/informal logic can be taught as a "contentless", context independent subject. John McPeck has been most prominent in the attack, Robert Ennis, Richard Paul and Harvey Siegel in the defence.37 McPeck maintains that (i) critical thinking cannot be reduced to a collection of subject-independent logical rules and that (ii) the evaluation of arguments involves context-dependent information. The information needed is not necessarily common knowledge, often being highly specialized. Moreover, what count as good reasons depends on the field in question, so even given the requisite, possibly context-dependent, information the criteria of evaluation may also depend on the context. McPeck's view makes transferability of critical thinking skills from one domain to another unlikely, though not impossible.

This would not be the proper context in which to evaluate McPeck's extensive writings and the large counter-literature even were I competent to do so. Two observations are in order, though. Firstly, while much disputed in North America McPeck's views are orthodoxy in the United Kingdom critical thinking/informal logic movement.38 Secondly, at least with respect to background information the context dependence is similar to the problems besetting the work on knowledge representation and expert systems in artificial intelligence mentioned in §2.3 above.

There is debate as to whether critical thinking is a skill or an ability or neither. John Passmore likens it to a character trait that is to be fostered.39 Others see critical thinking as an ability requiring, as McPeck would insist, understanding of particular disciplines, and not reducible to mastery of certain skills.40

Empirical tests on the teaching of critical thinking yield equivocal evidence, not least because it is far from clear that the numerous extant tests measure what they purport to measure and the experimental methodology is sometimes doubtful. Also, some tests deal with subject-specific teaching of critical thinking, not critical thinking as a transferable skill. Among claims made on the basis of empirical research are these: that just one year of university or college education, independently of discipline, suffices to enhance ability in critical thinking; that education in philosophy generally (i.e. philosophy, not logic) increases ability in critical thinking; that while conventional education does improve critical thinking, teaching reasoning skills improves it more except among those who think ably initially, who may be adversely affected. The testing methods used have come in for a good deal of empirical evaluation and theoretical criticism, not least from McPeck.

Tim van Gelder has surveyed various tests of the efficacy of critical thinking teaching and comes to admittedly tentative but none the less cautionary conclusions, of which these two stand out:

Currently it is difficult to make a convincing case—i.e., one that would survive hard scrutiny from good critical thinkers—that CT courses are of any substantial benefit. On one hand there are various studies indicating no significant benefit from CT instruction. On the other, there are some studies which do appear to find some benefit. The belief, common among CT teachers, that CT courses are better for improving CT than formal logic courses does not appear to be supported by the available evidence, such as it is.

Hardly surprising, then, that he draws the conclusion that 'there is a serious need for more and better research on this issue'.41

3.5 The fires that raged in the 1980s and early 1990s seem to have died down. The "Great Debate" seems to have fizzled out in dull compromise, recognition that

Different elements may be either general or specific in different ways on different occasions of their use. The issue is less whether there are general elements to be employed, but at which level of generality skills components are most effectively identified and at which level they are most efficacious for teaching and learning in different contexts.42 [T]here are general cognitive skills; but they always function in contextualized ways.43

Few experts in the field would now support the claim that universal thinking skills exist outside any context. Thinking skills are not an abstract logical structure. They are embodied practical skills that are learnt in a context and then, often with the help of teachers, taken out from that context to be applied in a new context. If these relatively general skills are taught in an abstract form, then careful work needs to be done by teachers to embed them in a context where they can be applied.[...]

Few experts in the field would now support the claim that there are universal thinking skills or completely general strategies for learning and problem solving. However there is consensus that there are a range of relatively general learning strategies that can be disembedded from some contexts and re-embedded again in new contexts.44

Critical thinking, informal logic and argumentation theory nowadays consort in more than merely peaceful co-existence.45 The point of raking over the coals again is to flag issues that must be addressed if one is to teach one or more of critical thinking/informal logic/argumentation theory, either in addition to or instead of formal logic. In the jargon of the moment, one must think through the teaching and learning aims and outcomes, and the methods appropriate to them.

For those who would substitute for the study of formal logic in the philosophy curriculum critical thinking, informal logic, or argumentation theory (or some melange of all three), one question must be addressed: is there anything in the nature of critical thinking, informal logic and argumentation theory that indicates that they are best pursued and/or taught by philosophers? Any answer takes a stand on the nature and content of these disciplines, a stand that is controversial in ways in which no parallel controversy attends formal logic. Van Eemeren says,

The study of argumentation is characterised by its interdisciplinary, or in any case multidisciplinary, character. Its progress depend on contributions from a great variety of fields: philosophy, logic, (speech) communication, linguistics, psychology, sociology, rhetoric, law, etc.46

All well and good, but who is going to teach this to philosophy undergraduates? (And why?)

The Summer 2000 issue of Informal Logic (issue 20/2) contains a series of essays on the relation of informal logic to philosophy: 'Informal Logic & Its Implications for Philosophy', by Alec Fisher; 'The Place of Informal Logic in Philosophy' by James B. Freeman, 'The Significance of Informal Logic for Philosophy' by David Hitchcock; 'How Philosophical is Informal Logic?' by John Woods. In part because proof, demonstrative argument, the construction of a certain kind of argumentation, is only one part of modern formal logic, questions about the philosophical significance and philosophical content of formal logic answer themselves; there is no need for the same kind of debate. Logic concerns not just inference but also implication, i.e. logical consequence: we infer; sentences or propositions imply others.47 How do inference and implication match up? Formally, soundness and completeness theorems tells us: perfectly. But which, if either, has primacy? That depends on the kind of theory of meaning one favours, truth conditional or something more inferential (conforming to the slogan "meaning is use"). Logical truths are usually taken to be a priori (for they can be established by reason alone, as completeness guarantees), but first-order logical truth is undecidable: so what is the nature of the norm that enjoins us to believe logical truths? Applied arithmetic, both addition and multiplication, can be mimicked in first-order logic with identity; what does this tell us about arithmetic and arithmetical knowledge? And then there are the more prosaic, less tractable issues: truth, vagueness, the indicative conditional.48

3.6 What may we conclude? Philosophy generally, and therein formal logic but only as one among equals, may improve the critical thinking of students although perhaps no more than other subjects. Logic, it seems, has no special role to play here. Informal logic, if differentiated from a more broadly conceived critical thinking, has to be taught with care if it is not to be merely an emasculated form of formal logic. Thus some formal logic seems to be a necessary ingredient for informal logic if it is to do more than catalogue rhetorical devices and fallacies. Moreover, if McPeck is even half right the evaluation of everyday arguments calls for rather more than any single course could reasonably be expected to teach in the way of specialized knowledge. And if much of artificial intelligence is not barking up the wrong tree, the theory behind the reasoning and argumentation of various disciplines is best analyzed from a starting point that takes for granted the methods and techniques of formal logic.

Philosophical logic and philosophy of logic are only the most obvious philosophical progeny of formal logic; it has been a wellspring of philosophical theorising. Critical thinking, informal logic, and argumentation theory do not promise half so much.

§4 The practice of logic teaching

4.1 The major difficulty faced in teaching formal logic is not, I submit, that the arguments it deals with are unnatural or unlike "real" arguments (although that may well be the case and for good reason);49 rather it is that in learning formal logic students have to learn how to think about abstract matters, i.e. to recognize patterns (or structures) and to think about the patterns themselves rather than their instantiations. In requiring this ability modern formal logic differs at most in degree from traditional logic but we must recognise that it is an ability that modern education and society does little to foster and hone. Carl Chung says,

From the point of view of most of our first-year students, logic is hard. It is hard because it is abstract, detailed, and rigorous in the context of a society that stresses the concrete, the soundbite, and the quick rhetorical conclusion.50

He reports Julie Gowen's alarming argument that 'up to forty percent of introductory logic students are unable to engage in abstract reasoning, since they are, according to the Perry scheme, "concrete operational thinkers"'.51 The literature on the Wason selection task might be taken to show that few of us naturally think at an abstract level (which, of course, isn't to say that such thinking cannot be learned by the majority).

From their pre-university education, students are most likely to encounter abstract reasoning in mathematics and, to a lesser extent, physics. There is plenty of anecdotal evidence that the level of abstract thinking systematically encountered in school mathematics has waned over the past quarter-century (despite an increased emphasis on the teaching and learning of thinking skills in secondary education!). Thus, if the anecdotal is more than merely anecdote, students come to university increasingly ill-prepared for engaging in the kind of thinking formal logic requires.

One thing is certain: the level of mathematical competence expected of first-year students taking logic courses has declined since Tarski wrote his Introduction to Logic and the Methodology of Deductive Sciences (1940) and Morris Cohen and Ernest Nagel wrote Book I, the logic part, of their An Introduction to Logic and Scientific Method (1934). It is not just the absence of natural deduction and/or truth-trees that makes it unlikely that any teacher of logic uses either of these as their basic text (although both have been re-issued in paperback in recent years): both presuppose rather more mathematical knowledge than any logic teacher would dare assume today.

4.2 Another difficulty faced in teaching logic as part of a philosophy curriculum is that students often come to the subject unaware of the nature of academic philosophy and, more particularly, the nature of formal logic. Some introductory texts make a fair job of indicating what logic is about, what its subject matter is, and how it is approached (e.g., Blackburn's Think, Teichman and Evans' Philosophy: A Beginner's Guide, Nuttall's Introduction to Philosophy), but perhaps it is the case that only a dedicated logic text can make clear what is really involved in a ten or twelve week long course in formal logic, what the experience of having to work at it will be like.

Teaching logic to arts and humanities students, another difficulty arises. Like mathematics and science courses, but unlike most arts and humanities courses, including other philosophy courses, logic is more or less relentlessly cumulative; it does not cover one topic then pass on to another independent one.

4.3 Like Carl Chung, Helen Beebee makes much of the difficulty some students experience in learning logic—or, in some cases, failing to learn it.52 Perhaps one should not make too much of this, for while certainly some students experience great difficulties, others find logic easy. The range of marks obtained in logic courses is much wider than the all-too-common bunching in the 2.i band that one finds in other philosophy courses. Of courses taught in arts and humanities faculties, only linguistics and some language courses manage to generate anything like the same spread. We should take pleasure in the high marks some students—and, it bears emphasising, not just those with a strong background in mathematics—achieve but it is of course the tail of low marks that causes the problems.

4.4 In response to the difficulty experienced by students and what she reports as an inability to retain even the most fundamental of ideas from their course in formal logic, Beebee advocates the dumbing down of introductory formal logic courses. There is in this suggestion a danger that imperils logic as practised by philosophers, imperils indeed the very existence of logic pursued as a branch of philosophy.53

Much of what is now taught in first-level courses becomes, if logic is dumbed down, second-level; what is currently second-level becomes graduate level. And many philosophy departments will not run logic courses at graduate level because, due to the increased specialisation at that level, there will be insufficient demand to justify putting them on. And so the really cool stuff in formal logic will disappear from the philosophy curriculum. But then departments won't need to employ logicians—people who really understand logic, who think about it, and who contribute to its development—because what little logic that remains can be taught by philosophers whose main interests lie elsewhere. And so interest and competence spiral down.

4.5 The dismal picture I have just painted runs counter to the Association for Symbolic Logic's 'Guidelines for Logic Education'.54 Moved by 'the increasingly technical demands placed on people by the information revolution [which] makes it all the more important that people understand basic logical principles of reasoning', the ASL recommends that all post-secondary education institutions should teach first-order logic, including formal proofs and discussion without proof of the soundness and completeness theorems, and that a course encompassing this material should be available to all students.55 If this proposal seems fanciful, we would do well to remember that philosophy graduates do get jobs on the strength of the transferable analytic skills their education is thought to impart. As far as some employers are concerned, their training in formal logic is by no means a negligible factor in this.56

Endnotes

  1. 'One reason why an understanding of logical notation [is] essential [is] the practical one that it is often used in the books and articles which students are required to read. Students would have a greater motivation to master the symbolism if it were used more often by non-logic teachers.' From the online report on the session 'Overcoming Fear of Formal Notation, and Making Logic More Attractive' at the PRS-LTSN's first Teaching Logic meeting, University of Leeds, 22nd February, 2002..
  2. William Brenner, Logic and Philosophy: An Integrated Introduction, University of Notre Dame Press, 1993.
  3. Helen Beebee, 'Introductory Formal Logic: Why do we do it?', Discourse: Learning and Teaching in Philosophical and Religious Studies, 3/1 (2003), 53-62.
  4. Alec Fisher, The Logic of Real Arguments, Cambridge University Press, 1988, p. vii.
  5. Alec Fisher, 'Re-engaging with Real Arguments', in A. Phillips Griffiths (ed.), The Impulse to Philosophise, Royal Institute of Philosophy Supplement: 33, Cambridge University Press, 1992, p. 90 (emphasis in the original).
  6. Morris Kline, 'Logic versus Pedagogy', American Mathematical Monthly, 77/3 (1970), 264-82.
  7. Fisher, 'Re-engaging ...', p. 107.
  8. Michael Resnik, 'Logic: Normative or Descriptive? The Ethics of Belief or a Branch of Psychology?', Philosophy of Science, 52 (1985), 221-38.
  9. See Wolfgang Carl, Frege's Theory of Sense and Reference: Its Origin and Scope, Cambridge University Press, 1994, Chapters 1 & 2, for an extended discussion of this aspect of Frege's philosophy of logic.
  10. Be it noted that in their recent textbook, Critical Thinking: A Concise Guide (Routledge, 2002), Tracy Bowell and Gary Kemp say (p. viii), We do not entirely accept the view that examples in a book on critical thinking should be real, or even realistic. [...] Unrealistic, trumped-up examples are often much more useful for illustrating isolated concepts and points of strategy.
  11. For introductions to the extensions of first-order logic used in the design of expert systems see Gerhard Brewka, Nonmonotonic Reasoning: Logical Foundations of Commonsense, Cambridge University Press, 1991, Brewka, Jürgen Dix and Kurt Konolige, Nonmonotonic Reasoning: An Overview (CSLI Lecture Notes, vol. 73), CSLI Publications, 1997, or Karl Schlechta, Nonmonotonic Logics: Basic Concepts, Results, and Techniques (Lecture Notes in Artificial Intelligence, vol. 1187), Springer, 1997. For a brief, nontechnical discussion of some of the issues see David Israel, 'The Role of Logic in Knowledge Representation', Computer, 16/10 (1983), 37-41.
  12. Paul Krause and Dominic Clark, Representing Uncertain Knowledge: An Artificial Intelligence Approach, Kluwer Academic Press and Intellect Books, 1993, p. 191 of the Intellect edition.
  13. Ryle's analogy came up again in the Leeds PRS-LTSN Teaching Logic meeting. In the online summary of 'Overcoming Fear of Formal Notation ...' it is reported, If students complained that logic cannot be applied directly to philosophical arguments, they could be told that it is like military drills, which are different from what you do in battle, but none the less necessary training. Fisher casts doubt on the aptness of the analogy, 'Re-engaging with Real Arguments', p. 94.
  14. On formal semantics, see, e.g., the papers collected in Paul Portner and Barbara H. Partee (eds.), Formal Semantics: The Essential Readings, Blackwell, 2002.
  15. See, e.g., Chaim Perelman and Lucie Olbrechts-Tyteca, The New Rhetoric: A Treatise on Argumentation, University of Notre Dame Press, 1969. (Translation of French original from 1958.)
  16. Fisher, 'Re-engaging ...', pp. 95 and 106-7.
  17. Informal logic stresses non-formal methods in analysis and evaluation. Thus Ralph Johnson and J. Anthony Blair said, By informal logic we mean to designate a branch of logic which is concerned to develop informal standards, criteria, procedures for the analysis, interpretation, evaluation, critique and construction of argumentation in everyday discourse. 'The Current State of Informal Logic and Critical Thinking', Informal Logic, 9/2-3 (1987), 147-51, p. 147. More recently they have described informal logic as 'a complex mix of practical and theoretical enterprises related to argument evaluation' ('Informal Logic in the Twentieth Century', in Douglas Walton and Alan Brinton (eds.), Historical Foundations of Informal Logic, Ashgate, 1997, p. 160). A "logic of argumentation" can be approached formally, in which case techniques and notations similar to those of orthodox formal logic return; see, e.g., F. van Eemeren et al., Handbook of Argumentation Theory, Foris, 1987, §3.4. Michael Gilbert gives a brief history of argumentation theory in Ch. 1 of his Coalescent Argumentation, Lawrence Erlbaum, 1997. For a recent overview of the discipline, see van Eemeren, 'Argumentation: an overview of theoretical approaches and research themes', Argumentation, Interpretation, Rhetoric (online journal) , issue 2 (2002) at http://www.argumentation.spb.ru/2002_1/papers/1_2002p4.html.
  18. John E. McPeck, Critical Thinking and Education, Robertson, 1981. In Ch. 4 the author contrasts critical thinking and informal logic.
  19. Mark Battersby, 'Critical Thinking as Applied Epistemology: Relocating Critical Thinking in the Philosophical Landscape', Informal Logic, 11/2 (1989), 91-100. Battersby, it should be noted, does not distinguish critical thinking from informal logic in this regard; in his opinion, informal logic should also be applied epistemology.
  20. Trudy Govier, A Practical Study of Argument, Wadsworth, 1985.
  21. Trudy Govier, 'Critical Thinking as Argument Analysis?', Argumentation, 3/2 (1989), 115-26.
  22. See, e.g., Harvey Siegel, 'Educating Reason: Critical Thinking, Informal Logic, and the Philosophy of Education', Informal Logic, 7/2-3 (1985), and 'Epistemology, Critical Thinking, and Critical Thinking Pedagogy', Argumentation 3/2 (1989), 127- 40.
  23. See, e.g., Ernest Marshall, 'Formalism, Fallacies, and the Teaching of Informal Logic', in F. van Eemeren et al. (eds.), Argumentation: Analysis and Practices, Foris, 1987, pp. 386-93.
  24. Gilbert, Coalescent Argumentation, p. 22. An overstatement to be sure, but one with more than a grain of truth in it. For a more nuanced account of the (evolving) content of informal logic see §§2 & 5 of Leo Groarke, "Informal Logic", The Stanford Encyclopedia of Philosophy (Winter 2003 Edition), Edward N.Zalta (ed.), http://plato.stanford.edu/archives/win2003/entries/logic-informal/ .
  25. Brenner, Logic and Philosophy, p. 89.
  26. Ideas as to which inferences are instances of fallacies and why have changed from Aristotle to the present day; there is also theoretical disagreement amongst contemporary theorists as to the nature of fallacies. See van Eemeren et al., Handbook ..., pp. 90-94. Intending, I believe, no distinction between critical thinking and informal logic, Claude Gratton, 'Counterexamples by Possible Conjunction and the Sufficiency of Premises', Teaching Philosophy, 26/1(2003), 57-81, pp. 57-8, complains that while producing counterexamples aplenty to demonstrate the fallaciousness of various fallacies 'a surprising number of critical thinking textbooks' offer little or nothing in the way of advice on the construction and evaluation of counterexamples. On why the evaluation of counterexamples is no simple matter see Adrian Heathcote, 'Abductive inference and invalidity', Theoria, 61/3 (1995), 231-260.
  27. Leo Groarke and Christopher Tindale, 'Critical Thinking: How to Teach Good Reasoning', Teaching Philosophy, 9/4 (1986), 301-17. Groarke and Tindale pursue this approach in their text-book, Good Reasoning Matters!: A Constructive Approach to Critical Thinking (third edition), Oxford University Press, 2004.
  28. See W. Kistner, 'A Note on Formal Logic in Teaching Critical Thinking', South African Journal of Philosophy, 7/2 (1988), 123-5.
  29. Douglas Walton, Informal Logic: A Handbook for Critical Argumentation, Cambridge University Press, 1989, p. xi.
  30. Gerhard Preyer and Dieter Mans, 'On Contemporary Developments in the Theory of Argumentation', ProtoSociology: An International Journal of Interdisciplinary Research, 13 (1999), 3-14, p. 3.
  31. McPeck, Critical Thinking in Education, pp. 67 & 68.
  32. John McPeck, Teaching Critical Thinking: Dialogue and Dialectic, Routledge, 1990, p. 122. This book comprises a selection of McPeck's articles, critical comments by Paul and Siegel inter alia, and McPeck's responses.
  33. Groarke, Informal Logic, introduction.
  34. See, e.g., Mark Weinstein, 'Critical Thinking: Expanding the Paradigm', Inquiry: Critical Thinking Across the Disciplines, XV/1 (1995), 23-39.
  35. McPeck, Critical Thinking in Education, p. 78.
  36. van Eemeren, 'Argumentation: an overview ...', §3.2. van Eemeren's strictures are perhaps too harsh. David Hitchcock, 'Relevance', Argumentation, 6 (1992), 251-70, provides an extended treatment of relevance although not one that lends itself to formal representation.
  37. See McPeck, Teaching Critical Thinking.
  38. As reported by Fisher, 'Effective Learning and the Critical Thinking Movement', in M. Coles and W. Robinson (eds.), Teaching Thinking: A Survey of Programmes in Education, Classical Press, 1991. The observation is endorsed by Victor Quinn, 'In Defence of Critical Thinking as a Subject: If McPeck is Wrong He is Wrong', Journal of Philosophy of Education, 28/1 (1994), 101-11, who argues against the orthodoxy. It is endorsed again, more recently, by Rupert Wegerif, Literature Review in Thinking Skills, Technology and Learning (NESTA Futurelab Report 2), NESTA Futurelab, 2002, p. 12, citing Stephen Johnson, Teaching Thinking Skills (IMPACT 8), Philosophy of Education Society of Great Britain, 2000, in support of the claim that 'in Britain something like this [McPeck's] position appears to have strong support amongst philosophers of education'.

     

  39. John Passmore, The Philosophy of Teaching, Harvard University Press, 1980, Ch. 9.
  40. See, e.g., Robin Barrow, 'Skills Talk', Journal of Philosophy of Education, 21/2 (1987), 187-95.
  41. Timothy van Gelder, 'The Efficacy of Undergraduate Critical Thinking Courses: A Survey in Progress',Preprint 1/2000, online at http://www.philosophy.unimelb.edu.au/reason/papers/efficacy.html. In reviewing the more general literature on the teaching of thinking skills in pre-university education, the same conclusion, that more research in the evaluation of programmes for teaching thinking skills is needed, was reached by John Nisbet, Teaching Thinking: an Introduction to the Research Literature (SCRE Spotlight, 26), Scottish Council for Research in Education, 1990, and, ten years later, by Valerie Wilson, Can Thinking Skills be Taught? (SCRE Spotlight, 79), Scottish Council for Research in Education, 2000. In 'Critical thinking: Some lessons learned', Adult Learning Commentary Number 12, 30 May 2001 (online at http://www.ala.asn.au/commentaries/2001/Gelder3005.pdf ), van Gelder briefly shares some of the lessons he has learned concerning the teaching of critical thinking.
  42. Mark Weinstein, 'Critical Thinking: The Great Debate', Educational Theory, 43/1 (1993), 694-720. The deeper issues that Weinstein identifies as still outstanding mesh to some extent with feminist concerns about logic, argument, and reason. See, e.g., Phyllis Rooney, 'Feminism and Argumentation: A Response to Govier', (online at http://venus.uwindsor.ca/faculty/arts/philosophy/ILat25/edited_rooney.doc), a paper presented at IL@25, University of Windsor, May 2003; see also, e.g., Rooney, 'Recent Work in Feminist Discussions of Reason', American Philosophical Quarterly, 31/1 (1994), 1-21, and the 'Symposium on Feminism and Reason', Australasian Journal of Philosophy, 71/4 (1993).
  43. David N. Perkins and Gavriel Salomon, 'Are Cognitive Skills Context-Bound?', Educational Researcher, 18/1 (1989), 16-25; cited in David Billing, 'Generic Cognitive Abilities in Higher Education: an international analysis of skills sought by stakeholders', Compare, 33/3 (2003), 335-350. Perkins and Salomon's much-cited article reviews empirical evidence regarding transfer of thinking skills. Billing summarises their findings in saying, 'General cognitive skills [sometimes called meta-cognitive skills] are tools for wielding domain-specific knowledge' (Billing, loc. cit.).
  44. Wegerif, Literature Review ..., pp. 13 & 20. Wegerif's report covers the teaching and learning of thinking skills at primary, secondary and tertiary levels. The skills debate rumbles on. For two recent contributions, see Geoffrey Hinchliffe, 'Situating Skills', Journal of Philosophy of Education, 36/2 (2002), 187-205, and Gerald Smith, 'Are There Domain-Specific Thinking Skills?', Journal of Philosophy of Education, 36/2 (2002), 207-227.
  45. See for example the papers presented at the IL@25 conference, a conference celebrating the twentyfifth anniversary of the First International Symposium on Informal Logic; the papers are available online at http://zeus.uwindsor.ca/faculty/arts/philosophy/ILat25/index.htm .
  46. 'Argumentation: an overview ...', §5.4
  47. See, e.g., John Corcoran, 'Conceptual Structure of Classical Logic', Philosophy and Phenomenological Research, 33/1 (1972-73), 25-47.
  48. The discoveries of late nineteenth and twentieth century mathematical logic have been of immense significance for the philosophy of mathematics—for the philosophy of mathematics, not for mathematical practice and only marginally for mathematical theory, given the breadth of mathematics. (A mathematical education can easily, and not improperly, leave the mathematics graduate entirely ignorant of mathematical logic.) Of course, in large measure because it presupposes these results in mathematical logic and, in addition, is best done by those who have some acquaintance with university level mathematics (just as the philosophy of physics is best done by those who have some acquaintance with university level physics and the philosophy of law is best done by those who have some acquaintance with legal theory and practice), the philosophy of mathematics is thought of as a narrow, high-level specialisation. This is unfortunate, because consideration of the very special nature of mathematics has important consequences for general metaphysics and, perhaps even more so, though this is even less recognised in undergraduate teaching and elsewhere, for epistemology: thinking about the infinite is a very special human accomplishment.
  49. The arguments considered in formal logic differ at most in the degree of their unnaturalness with what survives or natural, "real" arguments after analysis in informal logic. See, e.g., the examples throughout Fisher, The Logic of Real Arguments, and van Eemeren et al., Handbook ..., pp. 27-35.
  50. Carl Chung, 'Enhancing Introductory Symbolic Logic with Student-Centered Discussion Projects', Teaching Philosophy, 27/1 (2004), 45-59, p. 46.
  51. Julie Gowen, 'Can We Teach Introductory Logic?', Teaching Philosophy, 16/3 (1993), 237-48, p. 241. The Perry scheme, part of a theory of cognitive development, comes from William Perry, Forms of Intellectual and Ethical Development in the College Years: A Scheme, Holt, Rinehart and Winston, 1970.
  52. Beebee, 'Introductory Formal Logic ...'.
  53. There is also, I think, a hint of a suggestion that logic is unusual in that the basics are forgotten by students who have passed exams. I suspect this is not so. I could offer anecdotal evidence from my experience teaching other philosophy courses; instead I offer something rather better researched, namely E.M. Carson and J.R. Watson, 'Undergraduate Students' Understanding of Enthalpy Change', University Chemistry Education (The Journal of the Tertiary Education Group of the Royal Society of Chemistry), 3/2 (1999), 46-51.
  54. 'Guidelines for Logic Education', The Bulletin for Symbolic Logic, 1/1 (1995), 4- 7. The guidelines were prepared by the ASL’s Committee on Logic and Education.
  55. Guidelines ..., p. 5.
  56. 'Organisations such as the Council for Industry and Higher Education and the Association of Graduate Recruiters value philosophy graduates precisely because of their training in formal logic.' From 'The Way Forward', in the online report of the PRS-LTSN’s Leeds Teaching Logic meeting. Billing, 'Generic Cognitive Abilities ...', establishes a ranking of core skills and attributes as sought and/or valued by "stakeholders" (employers, mostly). What are called 'analytical, evaluative, logical and critical skills, conceptual thinking, and skilful diagnosis' rank ninth amongst UK stakeholders but come top in the USA.

Return to vol. 4 no. 1 index page

This page was originally on the website of The Subject Centre for Philosophical and Religious Studies. It was transfered here following the closure of the Subject Centre at the end of 2011.

-
The British Association for the Study of Religions
The Religious Studies Project