Education as Second Order

Paper read at the Annual Conference of the Society for Applied Philosophy, Mansfield College, Oxford, June 2002


Applied Philosophy

No doubt there are a variety of things that can properly be described as 'Applied Philosophy'. To begin this paper, I want to offer one candidate for that role.

A common theme, prominent for instance in Barry Stroud's recent reflections on the place of colour in our scheme of things (2000), is the thought that there are ordinary questions and there are what may look like the same questions but asked in a philosophical tone of voice or in a philosophical context, where ordinary answers are no longer appropriate. I want to turn this idea around to suggest that there are a number of claims that may or may not succeed in their philosophical contexts but which are plausible and instructive when taken in an everyday ordinary way.

An example of the kind of thing I am thinking of, but one which I do not intend to discuss further, is the tissue of claims relating to "private language" and the "private language argument", or rather, when dephilosophised, the thought that the languages we happen to speak are public entities, learnable by ordinary humans without telepathy or divine guidance, etc., etc. Philosophically people want conclusions here about what must be; but for a lot of the practical applications it is enough that things simply are so.

I shall be making use of a couple of other examples of philosophy made fit for ordinary consumption in the course of the paper. One additional feature of them will be that the invocation of the educational context will allow us to overlook possible deficiencies of the claims as simple truths about how things are. (I hope this is not just a matter of endorsing what Straughan and Wilson (1983) labelled "optimistic interpretations" - studying X will lead pupils to appreciate the diversity of cultures, when all that can be claimed is that studying X is intended so to do. It is uncomfortably close to that; perhaps I can excuse it as a matter of drawing out the normative content of a conception of education.)

Second Order/Meta-X

Another preliminary matter that could lead us astray, but which is, I think, worth at least noting, concerns the notion of 'second order' that I have used in the title. I believe my use of the notion to focus on, for instance, beliefs about beliefs, hopes about hopes, theories about how theories work, etc., is fairly standard. But it is perhaps worth trying to get clear on its relation to what I presume to be the origin of the terminology in formal logic.

In formal logic there is a distinction, confused in the usage I have adopted of 'second order', between second-order systems and metalogical matters. A convenient reference (Shapiro in Honderich, 1995, courtesy of Xrefer) tells us that second-order systems are those which, in addition to variables standing for objects, use variables that "range over sets, properties, functions, or propositional functions on the range of the first-order variables, the domain of discourse"1 while metalogic is "the mathematical and philosophical study of the components of systems of logic" which issues in claims about such matters as completeness or incompleteness, independence of axioms, or the indefinability of the quantifier most in ordinary first-order logic.

There is no direct link between these two items. We can study the metalogic of first-order logical systems; we can use second-order logic without a care for metalogical results.

But there is a route to seeing how they become entangled. In working within first-order logic, when "doing" logic, there are two ways of generalising: one may employ the apparatus of quantification over variables standing for first-order objects or one may use schematic letters. In a careful discussion of the contrast between variables and schematic letters, the Kneales in effect claim that using schematic letters is a way of making universal statements of second order, not universal statements within the first-order language. These universal statements of second order are implicitly metalogical statements about the first-order system.2

Several writers are keen to insist upon the very great difference that the explicit use of second-order variables makes when contrasted with implicit generalisations employing schematic letters. Grandy points out that using schematic letters to formulate a claim "requires that the fact be true at least for all subsets definable in the language" (1977, 116), a denumerable number of sets, whereas explicit second-order quantification is modelled in terms of all the non-denumerable sub-sets of the domain, and thus yields more expressive power. I for one would appreciate a clearer grasp of the way this difference actually works - to start at the first-order level, 'if A is a man then A is mortal' doesn't seem to commit me to much less than '(x)(if x is a man then x is mortal)' - but fortunately I think we can proceed despite my ignorance here. The basic point for this paper is in fact that 'second-order' is not really the right choice - what I shall be looking at are really 'meta' matters.

Indoctrination

This presentation has been scheduled in a session on indoctrination. One route in to my wider concerns that might then be appropriate is to consider what is needed to combat whatever tendencies to indoctrination may exist within an educational system.

In my own work I have been happy to follow Kleinig is seeing indoctrination as a matter of disabling learners: he sums up his discussion by characterising it as "teaching in which the beliefs, attitudes, values, etc. taught are held in such a way that they are no longer open to full rational assessment" (1982, 62). I have myself wanted to extend the indictment of educational systems to the much more pervasive form of miseducation which simply neglects to develop a person's capacity for full rational assessment,3 though there are of course murky issues hidden within our talk of "full" rational assessment.

However slippery "full" rational assessment may be, it is, I think, undeniable that one element in a desirable level of cognitive self-awareness is a realisation of the general accuracy of one's own perceptual and inferential practices.

Here we encounter a philosophical thesis ripe for general consumption in Michael Williams' recent reflections on knowledge. Williams is trying to set out the appropriate place for observational knowledge in his non-foundationalist, non-coherentist view of knowledge. It is not enough that a person makes reliable reports on his surroundings; thermometers often do as much. For an observation-report to enter the 'game of giving and asking for reasons' (a phrase he takes from Wilfrid Sellars) we must treat it as such a reason and we must do this responsibly. Responsibility here amounts to recognising when we are and when we are not reliable observers or reporters of whatever is in question. "To be capable of observational knowledge, it is not enough (as pure reliabilists imagine) simply to be a reliable reporter on this and that: a person must know something about how reliable he is" (2001, 175). This sort of reflective, epistemic self-knowledge requires competence in language and so is beyond animals and small children. Observation of apparently simple first-order facts requires a grasp of a multitude of general facts about the world - Williams illustrates this by noting that reliably saying 'car' when confronted with cars is not sufficient for decent observation of cars: we need to grasp an indefinite number of thoughts about what cars do and enable us to do. Understanding the conditions on reliability also requires a good deal of general knowledge (though it is important for Williams' purposes that this knowledge does not usually enter in as a further justificatory premise but can be simply presupposed). A result of all this is that we cannot have simple observational knowledge on its own; it is part of a package deal.

However attractive or disputable this picture may be,4 let us ignore Williams' philosophical targets. The basic point that epistemic responsibility involves a grasp of the conditions of the reliability, not only of observational but also of inferential behaviour, is surely undeniable. It is not enough to know the answers to exam questions; a secure knower must also grasp the support for those facts and theories, the way they hang together, the reasons why our present perspective is rationally preferable to earlier or alternative perspectives. These are matters of logical relations, of explanatory power, of philosophical perspective. But to say we need to attend to all this in addition to the particular facts and theories that we currently teach students has clear implications for educational practice.

On the one hand, we tend not to focus on such issues, neither each student's own reliability or the factors that influence such reliability, nor the factors that ought to weigh with us in evaluating the reliability of others (an increasingly important issue when everyone depends more and more on a mostly anonymous Internet).5 It would be salutary to expand on this by dealing separately with how much schooling explicitly deals with questions of reliable reporting and with questions of reliable inference. I have myself addressed in a number of earlier papers our lack of concern with inference, despite all the talk about how studying X will make people better at reasoning. And of course others have said the same. There is now a fairly active movement to promote such matters in the curricula at all levels of education (I am thinking of informal logic and critical thinking, Philosophy for Children, and such like). I suggest that the reliability of observers is even less attended to, though Norris has done some work in the area.

On the other hand, these matters of the factual nature of our epistemic position are, it seems to me, central to how we should try to resolve various contentious issues. So, in thinking about the educational place of teaching religion (not the anthropological study of religion), it seems to me that we ought to recognise the meta-level fact of lack of agreement across cultures and times, and lack of agreement on ways of resolving these disagreements in a non-question-begging manner.

I am not of course saying that because not everyone agrees with the Pope or your local Hindu pandit then what they affirm must be false. I am simply saying that it is a fact about their beliefs that not everyone with an interest in the relevant issues accepts them, or how to adjudicate among them, and that these are facts that they would do well to recognise and include among their formal teaching. They are certainly facts that any educational system should add to whatever of their formal teaching it passes on.

And of course not merely the fact of disagreement but the whole set of issues relating to reliability that Williams is pointing to. We may not be able to legislate that Catholic Encyclicals add a reliability rating in the way cigarette packets now offer health warnings, but it might be salutary if we could.6

It is important, I think, that this concern not be restricted to the usual suspects. It is important that our teaching of mathematics and physics and the rest display why alternative views of those issues have been rationally discredited (particularly, perhaps, those alternative views that are initially attractive to unsophisticated observers - see my 1989).

I want now to move to the general picture of education.

The General Picture: metalevel transformation

That picture, the notion that one of the things that matters most in educational processes is the acquiring of second-order capacities, is no doubt simplistic, but it is one that does not seem to have been given much of a run for its money.7

Philosophy of education has trafficked in metaphors for education. Peters notoriously offered us initiation; earlier Dewey had espoused development. For those with a taste for the apparently incoherent, we have self-actualisation.

A recent inspiration for my present offering of transformation as another metaphor derives from Julia Annas' work on Platonic Ethics (1999): there she stresses the importance of a strand of thought in Plato that attends to the way ethical reflection transforms a person's conception of his or her goals. This provides an analogy for the deep changes that successful education achieves, changes that I had earlier argued (1995) undermine the applicability of our usual model of evaluative justification, a model which presumes substantial identity of the person involved. One difficulty we have in justifying education arises from the fact that the successfully educated person we are justifying it to is sufficiently different from what he or she may have been prior to education or without it, that ordinary justification is inapplicable.

Educational transformations may not be the same as Plato's virtuous transformation away from the things of this world to an extreme asceticism, but they involve an analogous reconstruction of values and commitments.

But it is not so much transformation as its modality that I want to advertise. The key idea that I want to set before you was central to Nerlich's work on value (1989), and indeed had flourished much earlier in a famous article by Harry Frankfurt (1971). So here we have the second philosophical thesis I want to offer for everyday consumption. Frankfurt had suggested that the distinguishing mark of a moral agent is that he or she is not 'wanton', that is to say, lacking in second-order volitions. A moral agent can choose among the desires that move to action. Moral agency, then, is a capacity to pick and choose among the desires one has; a second-order capacity focused on first-order inclinations.

When we look at inclinations to believe or accept propositions, this second-order capacity, construed as we hope it will be, yields the same concern for reliability we have briefly considered in relation to Williams. It connects with slogans about learning to learn that educators offer us - we must presume that epistemically responsible learning is in question, not learning from bar-room gossip or sensational magazines. So we are being told that an important aim is to get students to know how to acquire new beliefs in an epistemically responsible way, attentive to questions of evidential support, coherence with other well-founded beliefs, internal consistency, and so on. Thus Charles Bailey talks of teaching for evidence in opposition to indoctrinatory activity and suggests that good teaching will yield "insight into this kind of evidence that makes belief in such information warrantable, at least for the time being" (1984, p. 130). But if we should teach why this evidence makes this view the best supported among our current options, we need to do more than simply teach the view and the evidence for it. We need to consider questions of comparative confirmation as well. So we will be focusing on how our beliefs hang together, on the relations between their components, i.e. meta- issues.

There is some reason to think that if one wants to teach X it is usually better to teach X rather than Y (with the usual Elsterian exceptions). So if one wants to teach principles of comparative confirmation, perhaps we should teach principles of comparative confirmation, and not just offer examples. When one uses Socrates to illustrate (however cack-handedly) a syllogism in Barbara, it is easy to suppose people realise that the rule applies generally; when one teaches a bit of physics it is not so easy to discern the general methodological or legitimating lesson it might embody. As so many have said, we have to make the teaching focus more explicitly on the general points we hope people will take from it. One cause of our troubles is that usually we do also want people to learn the particular physics in a way we do not care about them learning "facts" about Socrates. So we will need to go over the same ground twice, once for its first-order content and then for what it reveals at the meta-level. A second practical problem is that most of the teachers to whom we entrust this work have never explicitly studied the second-order material.

When educators turn to matters of high culture, the attitude again is focused on the content of the canon (or the various canons now invoked) rather than on the importance of cultivating what are in fact second-order attitudes and dispositions in the learner, ways of reconstructing or transforming oneself. So the English National Curriculum Key Stages 3 and 4 for English offers us under 'English literary heritage':

Pupils should be taught:

Two items on the texts themselves (to which we can add several aims relating to 'understanding the author's craft' and other facets of interpretation) with one that leaves indeterminate what the importance of the texts might be. To appeal to one American critic, Bloom tells us that literature doesn't teach values but it teaches distrust of values, insight into their limitations, a reflective (i.e. second-order or meta-level) awareness of one's place in the world. So one defensible interpretation of (c) above would be the kind of second-order anti-wantonness we have mentioned. But it is clear that no stress is being laid here on encouraging students to undertake their own reflections and transformations; it reads more as if they will simply take note of what others have decided are important lessons.

One modest benefit of my proposed perspective is that it can perhaps set to rest the anxieties of those teachers who worry that they might be "imposing" values on their pupils. No doubt they often are, and schools intend so to do. But if we approach the question as one of encouraging self-definition, a disposition to resolve conflicts among first-order desires and imperatives in one way rather than another, we can recognise that the person "imposed" upon is ultimately the one who must do the choosing. What we can do to help is to offer a wider range of considerations upon which to reflect.

Nerlich can be seen as stressing the way in which all people (he prefers to speak of persons - and we can presume the usual exceptions for the severely mentally disabled) are confronted by the need to choose among conflicting desires and are offered by their cultures patterns for personal change over the course of their lives. One might say that implicit in playing at mummies and daddies is a realisation that life will not all be play, that one day the players will be expected to behave differently. Personal change here amounts to fairly deep changes in ways of thinking, ways of valuing, ways of behaving. Very early on in his book he says "to be a person .... means being in touch with the ideals and aspirations, with the task.... Anyone in that state will understand and even take some part in ... evaluating and transforming himself - excelling what he presently is" (1989, 2).

I do not have time now to enter into the rich texture of Nerlich's discussion, so must content myself with a couple of brief reactions.

One is that there are of course degrees of explicitness, of self-awareness. I can believe that for some people the understanding Nerlich speaks of hardly reaches consciousness; they change but without recognising the changes, unless perhaps some time after they have happened. Living a life has changed them rather than they having changed themselves.

But even if Nerlich's position needs to be somewhat qualified as the philosophical anthropology that it set out to be, it can be retained in pristine strength when we consider what ought to be required of educational practices. What we want in education is that a person revise their beliefs, their beliefs about their beliefs and how they are supported, their commitments, values, and inclinations. As Nerlich says, stressing the need for second-order style rather than one-off decisions, "the ground-floor problems of value for persons do not lie in which acts to perform but in which life to lead; the basic practical question is not what one shall do but what one shall be" (1989, 16). We want them to undertake this work as far as possible with eyes open, rather than it happening to them. Transformation may not always require the loss of earlier items - one may continue to enjoy fish and chips after having discovered quenelles de brochet - but one's set of desires will at least be different and differently structured.

A second comment concerns the directedness of Nerlich's 'self-excelling'. The task that Nerlich speaks of is a matter of desiring that some first-order desires or ways of coming to believe or what-have-you take precedence over other first-order desires or ways of coming to believe. It is the task of not being wanton. But as a matter of the abstract logic of the situation there are clearly alternative ways of achieving this. First-order A may triumph over B, but equally B may triumph over A. Moving up a level does not get rid of incompatible alternatives or of problems about objective backing.

One enormously large question is whether there are any directions of change that are better supported than others. If one values explanatory truth, or minimum standards of the quality of life for all people, then it would seem that there are transformations that conduce to (your contributing your mite to the achievement of) those ends and others that don't. It would, however, be a commission of the naturalistic fallacy to suppose that those or similar values are themselves simply given. Nerlich hopes to show that the human condition is so constrained, or at least can be evaluated by reference to the fullness of personal life that it manifests. He appeals to what one's culture offers but also wants to evaluate these cultural resources themselves, taking a culture as a more or less successful "engineering programme for producing persons" (1989, 17). I am not convinced this rejigging of Aristotelian eudaimonia can be sustained, however attractive it sounds. If Nerlich has not succeeded in establishing the requisite sense of objectively correct patterns of self-transformation that his project requires, we may have to return to the view I associate particularly with John Anderson: that the patterns of self-transformation typical of our educational traditions are simply one set among many ways of overcoming wantonness (not to mention, ignoring the whole issue). But these are among the largest questions of philosophy. I want to suggest much more modestly that recognising the logical structure of what we want education to achieve may do something for the coherence of our thoughts about it, and may conduce to clearer action to realise it.

References

Annas, J. 1999. Platonic Ethics, Old and New (Ithaca, Cornell University Press).

Bailey, C. 1984. Beyond the Present and the Particular (London, Routledge).

Brandon, E.P. 1989. "Subverting Common Sense: Textbooks and Scientific Theory," in Herget, D.E. (ed.), The History and Philosophy of Science in Science Teaching: Proceedings of the First International Conference, pp. 30-40 (Tallahassee: Science Education and Department of Philosophy, Florida State University).

Brandon, E.P. 1992. Steps Towards a Logical Geography of Education (Cave Hill, UWI Distance Teaching Experiment).

Brandon, E.P. 1995. "The Unjustifiability of Education," Studies in Philosophy and Education, 14, 217-227.

Brandon, E.P. 1997 "Education and Secularization: Taking Philosophy of Education Seriously," Caribbean Journal of Education, 19, 227-238, 1997.

Ellett, F.S. & Ericson, D.P. (1999) "Yes... But is it a Naturalism?" in Steven Tozer (ed.) Philosophy of Education 1998 (Urbana, Philosophy of Education Society).

Frankfurt, Harry G. 1971. "Freedom of the Will and the Concept of a Person," Journal of Philosophy 68: 5-20.

Gabbay, D. and Guenther, F. (eds.) 1983. Handbook of Philosophical Logic, Volume 1 (Dordrecht: Reidel).

Grandy, R. 1977. Advanced Logic for Applications (Dordrecht: Reidel).

Hamm, C. 1989. Philosophical Issues in Education (Lewes, Falmer).

Honderich, T. (ed.) 1995. The Oxford Companion to Philosophy (Oxford: Oxford University Press).

Kleinig, J. 1982. Philosophical Issues in Education (London: Croom Helm).

Kneale, W. & Kneale, M. 1962. The Development of Logic (Oxford: Clarendon Press).

Nerlich, G. 1989. Values and Valuing (Oxford: Clarendon Press).

Straughan, R. & Wilson, J. 1983. Philosophizing about Education (London: Holt, Rinehart and Winston).

Stroud, B. 2000. The Quest for Reality (Oxford: Oxford University Press).

Williams, M. 2001. Problems of Knowledge (Oxford: Oxford University Press).

Endnotes

1 It will not come as a surprise that even in logic the first order/second order distinction is not as clear-cut as it might be (v. Hodges' chapter in Gabbay and Guenther, 1983, 83-85); but this characterisation is widely endorsed and fairly usable.

2 In speaking of Frege's account of modus ponens, they say "the letters are free variables .... But ... they do not belong properly to his concept script. Their work is not to express universality in statements of that script, but rather to express universality in statements about statements of that script" (1962, 514). A bit later they say they are not syntactic or metalinguistic variables but "abbreviations for any signs or sign-complexes of suitable type which the reader may select from the basic script.... They are a device of second-order discourse" (516).

3 My reflections on Kleinig were offered in a distance education package for Education students at the University of the West Indies (1992) and are now accessible on the Cave Hill server (http://www.uwichill.edu.bb/bnccde/epb/stepsindoct.html).

4 One might note that, though there is probably no reason to regard cats as making reports on their observations, it does seem that they observe mice and that their perceptual states are serving to make their behaviour appropriate in a similar way to that which leads foundationalists to give a special place to our own perceptual experience.

5 A quick glance at the National Curriculum (using its website www.nc.uk.net) has, however, thrown up a few objectives that fall under this umbrella: Science Key Stage 4 Single subject includes these:

2(d) consider key factors that need to be taken into account when collecting evidence, and how evidence can be collected in contexts [for example, fieldwork, surveys] in which the variables cannot readily be controlled.
(i) judge the level of uncertainty in observations and measurements.
(n) explain to what extent these conclusions support any prediction made, and enable further predictions to be made.
(p) consider anomalous data giving reasons for rejecting or accepting them, and consider the reliability of data in terms of the uncertainty of measurements and observations.
(q) consider whether the evidence collected is sufficient to support any conclusions or interpretations made.
History Key Stage 3 has this:
4(b) evaluate the sources used, select and record information relevant to the enquiry and reach conclusions.
Of course, one needs to undertake some observations of one's own to discover how these objectives are actually realised in the classroom.

6 I have offered some fanciful thoughts on what the effects might be in my 1997.

7 Kleinig, for instance, has two passing references to Frankfurt's work but he does not carry over the second-order notion to his fairly extensive discussions of education. Hamm, to mention a writer who has published since Frankfurt's work, has nothing pertinent (1989). There is some discussion of a first/second order contrast in an exchange between Ellett and Ericson on the one hand and Siegel on the other at the 1998 US Philosophy of Education conference. But both parties seem to agree on aligning the contrast with that between claims and their normative justification. Thus Ellett and Ericson characterise the contrast in this way:

First-order questions are questions about the way the world is, while second-order questions are questions about the right use of the concepts of reality and knowledge decided in the most responsible way we can manage. Thus, the concern of second-order philosophical questions is legitimation (1999, 237-8).
Siegel seems to endorse this account. No doubt such issues are particularly important, but there can be straightforward second-order non-normative truths as well.

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Last revised 3rd September 2002.