Abstract
In recent work on truth and truthmaking, D. M. Armstrong has defended a version of ‘truthmaker necessitarianism’, the doctrine that truths necessitate truthmakers. Truthmaker necessitarianism, he contends, requires the postulation of ‘totality facts’, which serve as ingredients of truthmakers for general truths and negative truths, and propositions, which function as the fundamental truth bearers. I argue that neither totality facts nor propositions need figure in an account of truthmaking, and suggest that both are artifacts stemming, albeit in different ways, from an ontologically shady ‘linguisticizing’ tendency to conflate features of descriptions and features of what is described.
The world is all that is the case. The world is the totality of facts, not of things. The world is determined by the facts, and by their being all the facts. For the totality of facts determines what is the case, and also whatever is not the case.
I do not think that one can doubt that there are general facts. It is perfectly clear, I think, that when you have enumerated all the atomic facts in the world, it is a further fact about the world that those are all the atomic facts there are about the world, and that is just as much an objective fact about the world as any of them are. It is clear, I think, that you must admit general facts as distinct from and over and above particular facts.
Linguisticism Footnote2
Throughout the twentieth century, philosophy in Australia exhibited a notable quotient of independent-mindedness. Australia has produced its share of party-liners, but an impressive number of Australian philosophers have managed to buck prevailing trends and produce original, ground-breaking, philosophy. The philosophy has tended to be realist in character; the philosophers have exuded ontological candour. In recent years, globalization has set in, and with it, standardization of product. The distinctive tone of Australian philosophy is slowly giving way to the philosophical equivalent of Starbucks that characterizes so much mainstream philosophy today.
As we savour our lattes, let us pause briefly and give thanks for David Armstrong. Armstrong certainly belongs among the Pantheon of Australian Philosophers that includes the three Johns—Anderson, Mackie, Smart—and, I would add, C. B. Martin. Educated at Sydney, Armstrong managed, despite a sojourn at Oxford, to resist the linguistic turn and plot his own course. The result has been a remarkable and wide-ranging body of work presented with a clarity of style, a lack of pretension, and a disdain for self-conscious technical flourishes that beautifully reflects what we outsiders think of as the Australian character.
Even the most independent-minded thinker can occasionally succumb to prevailing doctrine, however. This can happen when ways of thinking have become so much a part of the atmosphere that their influence is largely invisible. So it is that philosophers wholly unsympathetic to the ‘linguisticization’ of metaphysics can yield to linguisticizing pressures. This, at any rate, is how I see Armstrong's treatment of two topics in his recent work on truthmaking. The first of these, Armstrong's commitment to the totality fact is, I will suggest, grounded in a tendency to conflate the world and descriptions of the world. The second, Armstrong's surprising acceptance of propositions as intermediaries hovering between the world and our talk about the world, stems from considerations of the kind that animate linguisticism, the idea that ontology is a branch of the philosophy of language. We can live without totality facts and propositions and, I shall argue, so can Armstrong.
Totality facts
Suppose you are partial to the idea that truths require truthmakers. ‘Snow is white’ is true, it would seem, in virtue of snow's being white. Here we have an instance of a contingently true English sentence. The sentence's truth depends in some way on how things stand in the world. Armstrong puts this by saying that a state of affairs, snow's being white, ‘necessitates’ its truth bearer. It would be incredible to think that snow's being white necessitates an English sentence, however, or any sentence at all. Thus, according to Armstrong, what is necessitated is not a sentence but a true proposition. The corresponding sentence is true derivatively: by virtue of ‘expressing’ this true proposition.
I say more about propositions below. For the moment I want to focus on the necessitation relation Armstrong takes to hold between truthmakers and truths. Suppose you thought of the necessitation of truths by truthmakers as entailment. According to John Bigelow, for instance, ‘Whenever something is true, there must be something whose existence entails that it is true. The “making” in “making true” is essentially logical entailment’ 1988: 125]. Footnote3
One problem for any such conception of truthmaking is that entailment, as standardly understood, is a relation between truth bearers: if p entails q, then p cannot be true if q is false. What we require, however, is a relation between truth bearers and something else, something non-representational.
You might try to sidestep this problem by imagining that the entailment holds between truths and descriptions—especially perspicuous descriptions, perhaps—of truthmakers. Bigelow, for instance, holds that the truthmaking relation ‘should not be construed as saying that an object entails a truth; rather it requires that the proposition that the object exists entails the truth’ Citation1988: 126]. But now we have the problem of the relation borne by the propositions or privileged descriptions that do the entailing and their truthmakers: to do their jobs, the entailing propositions will need to be true. It is hard to see how any such strategy could be thought to shed light on the truthmaking relation.
Armstrong agrees.
The first thing to notice is that the necessitation cannot be any form of entailment. Both terms of an entailment relation must be propositions, but the truthmaking term of the truthmaking relation is a portion of reality, and, in general at least, portions of reality are not propositions.
So the relation between truthmakers and truth bearers is a species of necessitation other than entailment. When we turn to Armstrong's discussion of totality facts, however, matters are less clear. Indeed, it looks as though the chief argument for the need for a totality fact is driven by a conception of truthmaking that conflates truthmakers with descriptions of truthmakers, and truthmaking with entailment: creeping linguisticism.
Armstrong, citing Russell, contends that ‘we cannot get away from recognising “general facts”’ Citation1997: 197]. We need general facts, totality states of affairs, to provide truthmakers for general truths and negative truths. Footnote4 All people are mortal. What might the truthmaker be for this truth? Imagine a list of all the people there are, have been, or will be, and suppose that each person on this list is mortal. Would this fact, the fact that every person on the list was mortal, serve to make ‘All people are mortal’ true? It would seem not. Imagine a world like ours but for the addition of a single non-mortal person. It would be true in that world that all the people on our list are mortal, but not true that all people are mortal.
We can cope with this difficulty by adding to our list a ‘that's all’ clause: ‘this is all the people’. Our list, together with the ‘that's all’ clause, does necessitate the truth of ‘All people are mortal’. Indeed, the list plus the clause entails this truth.
Speaking of lists and clauses is to speak at the level of truths, not the level of truthmakers. But Armstrong's idea is that we need something in the world answering to the ‘that's all’ clause if we are to have a truthmaker for our general claim.
This line of reasoning can be extended to negative truths. Suppose there are five pencils in your desk drawer. Does this fact necessitate the truth of the claim that there are no pens in the drawer? No; pens could be present in the drawer alongside the pencils. Suppose, however, that there are five pencils in your desk drawer and that's all. This would necessitate the negative truth: there are no pens in the drawer—and endless other negative truths: there are no lizards in the drawer, no snowballs in the drawer, no vials of aqua regia in the drawer. But what might the truthmaker be for the claim that there are five pencils in the drawer and that's all? Not, it would seem, solely the state of affairs of there being five pencils in the drawer. That state of affairs could obtain and, owing to the presence of other items in the drawer, the statement that there are five pencils in the drawer and that's all would be false.
It looks as though we need something in addition to the drawer and its five pencils if we are to have a truthmaker for our original assertion that there are no pens in the drawer. Suppose the five pencils are accompanied by a totality state of affairs, a ‘that's all’ fact. Now we have all we need to serve as truthmaker, not merely for our negative existential, but for assorted truths, including ‘There are exactly five pencils in the drawer’, ‘Nothing, other than pencils is in the drawer’.
Armstrong puts it this way.
If it is true that a certain conjunction of states of affairs is all the states of affairs, then this is only true because there are no more of them. If there are more, then the proposition is not true. That there are no more of them must then somehow be brought into the truthmaker. But to say that there are no more of them is to say that they are all the states of affairs. This, then, must be brought within the truthmaker. The truthmaker must be the fact or state of affairs that the great conjunction is all the states of affairs.
If we are to have an adequate truthmaker for universal or negative assertions, then, we must ‘bring within’ the world a totality state of affairs. But what exactly is a totality state of affairs? Consider a collection of objects, the nine planets, for instance, and assume that this is all the planets. This collection, Armstrong would say, stands in a ‘totalling’ relation to the property of being a planet. So the state of affairs of this being all the planets is the planets' standing in the totalling relation to the property of being a planet. The big totality fact would be the states of affairs making up the world standing the totalling relation to the property of being a state of affairs. Footnote5
One virtue of the ur totality state of affairs is its obviating the need for either additional lesser totalities or negative states of affairs. Suppose there are a dozen apples in the basket (and nothing more). Call this state of affairs A, and assume that A is part of the great conjunction of states of affairs plus the totality fact. Call the state of affairs that is the great conjunction plus the totality fact T. Given T, A, the state of affairs that there are a dozen apples in the basket and no more supervenes; given T, the truth of ‘there are no onions in the basket’ is guaranteed. Armstrong puts it this way: ‘the one embracing totality fact…entails all the lesser totality facts’ Citation1997: 201].
Parallel reasoning leads to the conclusion that we can dispense with a special class of negative states of affairs to serve as truthmakers for negative existential claims. What makes it true that there are no Arctic penguins is the Arctic as it is (devoid of penguins) plus the ‘that's all’ fact.
Given totality facts, and in particular the all-embracing state of affairs of totality, then it is easy to see that all negative states of affairs supervene. So we do not need negative states of affairs in the basic ontology in addition to totality states of affairs. We can have…negative truths, but their truthmakers are always positive states of affairs plus some state of affairs of totality.
General facts, because they set a limit, are themselves a species of negative fact. There is no getting away from negativity altogether. But general facts (states of affairs) seem to remove the need at least to postulate any further negative truthmakers.
Putting it colourfully, if God decrees a certain body of first-order positive states of affairs and then decrees that these are enough, there seems no need for him to establish first-order negative properties or states of affairs in addition. The first-order negative properties can certainly be said to be real. It is a fact in the ordinary sense of the word ‘fact’ that this swan on the Swan River in West Australia is not white-plumaged. But such facts seem to be no addition of being to general states of affairs.
One worry you might have is that an appeal to totality facts leads to an unhappy regress. Footnote6 Consider the aggregate, A, consisting of all the lower-order states of affairs. Add to this aggregate a totality state of affairs. We have a new aggregate, A′: the lower-order states of affairs plus the totality state of affairs. But A′ now stands in need of a totality state of affairs. We can add a new totality state of affairs for A′, but by so doing we merely create yet another aggregate state of affairs, A″, that will need totalling.
Does an objectionable regress threaten? No, says Armstrong.
The first totality state of affairs is a contingent state of affairs. [The totality might have been different.] But the further alleged totality states of affairs after this point are all entailed by the first totality fact….The further states of affairs supervene and further involve no increase of being.
have a regress of truths. But we know from the general theory of truthmaking that different truths can all have the same truthmaker. So I suggest that what we have here, after the first collector, is no more than a series of truths which all have the very same truthmaking state of affairs, viz. the original ‘Russellian’ totality state of affairs. The necessity of each step after the first at least suggests that no increase of being is involved.
The truth regress, Armstrong holds, is innocuous. Suppose p is true. Then it is true that p is true, and true that it is true that p is true, and so on. Do we require distinct truthmakers for all these higher-order truths? Perhaps not. Perhaps all of these truths have one and the same truthmaker, namely the truthmaker for p.
One striking feature of this line of response is that it appears to compromise the idea that the original totality state of affairs is something in addition to the states of affairs it ‘totals’. If it is an additional state of affairs, then there would indeed seem to be a new total: the lower-order states of affairs plus the totality state of affairs. If this second totality is no addition of being, however, why is the first? In the case of the truth regress, the truthmaker for ‘p is true’ is not something in addition to the truthmaker for p. Footnote7
Considerations of this sort push us toward the shocking idea that totality states of affairs are not, after all, additions of being. You might be nudged further along this path by considering the following question: could there be two worlds that differed in just one respect: one has and one lacks a totality fact? Differently put: suppose God, in creating the states of affairs constituting our world, had, for reasons of His own, neglected to add in the totality state of affairs, had failed to ‘decree that these are enough’. Would there be no general truths? No negative truths? Armstrong regards these possibilities as ‘clearly silly’.
It is important to remember that totality facts are higher-order facts, with lower-order entities that the totality facts ‘collect’ being a constituent of the totality fact. There are indefinite numbers of possible worlds where the lower-order entities exist just as they do in the actual world, but do not constitute the totality of being. These are those possible worlds that have the actual world as a proper part. It is these worlds that constitute the proper contrast with the actual world. They give us worlds where the actual totality fact is missing.
It is hard to see why a response of this kind does not beg the question against anyone who thought that totality facts supervene. This impression is reinforced in light of what Armstrong says about the necessity of totality states of affairs.
There must be a totality state of affairs for the world. Of a certain something, it is true that this is all there is. That it is true of this something is contingent. The totality might have been more, it might have been less. But that a totality fact exists appears to be necessary. So something, the fact that there must be a totality-fact for the world, supervenes.
In the case of the totality state of affairs, there is no one state of affairs that supervenes. The actual totality state of affairs might not have obtained. It does not supervene. So I can perhaps argue that what supervenes here, viz. that there must be some totality fact, is a trivial truth that involves no increase of being.
Here we confront a puzzle. Given some contingent totality, its being a totality supervenes, but its being this totality does not. In the usual case, determinables supervene on determinates. Suppose an object, o, is 10 metres square. Then o's being square and o's being four-sided supervene on o's being ten metres square. A natural way to understand this claim is that o is square or four-sided in virtue of being ten metres square. The truthmaker for ‘o is square’ and ‘o is four-sided’ is o's being ten metres square. Determinable truths are made true by determinate truthmakers.
Matters are otherwise in the totality case. It is not that something's being a totality supervenes on its being some determinate totality. Its being a totality is in some way prior to its being a determinate totality. How is this supposed to work? Whatever it is about a particular totality that necessitates its being a totality would seem to necessitate, as well, its being this totality.
This, in fact, is my suggestion. The totality state of affairs is an artefact. When we describe a totality, unless we include a ‘that's all’ clause, we leave it open whether what we have described is a totality or merely a component of some larger totality. Suppose Armstrong is right: the world is a world of states of affairs. Now suppose we describe the great conjunction of the states of affairs. Unless our description includes a ‘that's all’ clause, this description is compatible with there being additional states of affairs. A complete description of the world would not signal its completeness without an accompanying ‘that's all’ clause. Nor would such a description (minus the ‘that's all’ clause) entail the negative truths. But these facts are facts about our description, not worldly facts.
Imagine God's creating the world. If Armstrong is right, God will do so by creating all the actual states of affairs. Once the states of affairs are created, God rests. God has created the big conjunction of states of affairs, and this state of affairs is the totality of states of affairs. The totality supervenes. We can miss this seemingly obvious point if we run together descriptions of the world and the world. Armstrong's admission that there being a totality supervenes is a tacit recognition of this point.
Any description we give of the world in the course of offering a metaphysical theory will need a ‘that's all’ clause to be complete. This makes it look as though we need an additional ‘that's all’ truthmaker. But once we see that the construction of a totality, even the Big Totality, requires only the construction of the totality's constituents—all of them—we can see that the ‘that's all’ fact is a rhetorical flourish, something linguistically, not ontologically necessitated. We can allow totality states of affairs without supposing that they amount to an addition of being, something ‘over and above’ the totalities. Totalities speak for themselves.
Propositions
Armstrong's ‘truthmaker necessitarianism’ commits him to the idea that truthmakers necessitate truths. But truths require truth bearers. If there are endless truthmakers, and these necessitate endless truths, then there are endless truth bearers. What are the truth bearers? Armstrong rejects a number of candidates: sentences, utterances, statements, judgements, beliefs. We say such things are true or false, but, he contends, this is only because they express propositions that are themselves true or false. The basic truth bearers are propositions.
It is not altogether clear from Armstrong's discussion 2004: §2.6] what propositions are, but whatever they are they must be the sorts of thing that could be true or false. This seems to rule out propositions being sets of possible worlds or other nonrepresentational states of affairs. Nor are propositions abstract entities 2004: 12]. On the positive side, propositions are ‘intentional objects’ of beliefs, statements, and the like. Beliefs and statements are beliefs and statements that something is the case. What is believed or said to be the case is the ‘intentional object’ of the belief or utterance, and this, according to Armstrong, is a proposition 2004: 13].
If you believe that the cat is on the mat, then what you believe, your belief's intentional object, is that the cat is on the mat. This is a proposition. You might think that the proposition here is the state of affairs: the cat's being on the mat. But that cannot be right. The proposition, whatever it is, is true (or false) and the cat's being on the mat is neither. Armstrong says that propositions are
abstractions, but not in any other-worldly sort of sense of ‘abstraction’, from beliefs, statements, and so on. They are the content of the belief, what makes the belief the particular belief that it is; or else the meaning of the statement, what makes the statement the particular statement that it is.
Contents are types, universals, not tokens. ‘Contents and meanings seem to be properties, though they are doubtless not purely intrinsic (non-relational) properties of token beliefs and token statements’ [2004: 13]. So propositions are universals necessitated by states of affairs that serve as their truthmakers. Given Armstrong's rejection of abstract entities and uninstantiated universals, the theory will need to be modified to accommodate the legions of truths that have never been and never will be entertained by intelligent agents.
This…requires that we now modify the suggested account of propositions as intentional objects. Actual intentional objects require actual beliefs, actual statements and suchlike, and the world cannot necessitate such actualities. So we need an account of propositions that abstracts from whether or not they are expressed.
cover the cases of unexpressed propositions by treating them as possibilities, mere possibilities, of believing, or contemplating or linguistically expressing the unexpressed proposition.
Rather than following Armstrong into these rarified domains, we might consider a weaker form of truthmaker necessitarianism: truthmakers necessitate the truth of truth bearers. What is necessitated is not the truth bearer, but the truth bearer's truth. This sounds vaguely circular but the point would be that, given some representation, if that representation is true, then its being true is necessitated by whatever it is that makes it true. This is consistent with Armstrong's contention that the truthmaking relation is internal: given the relata, the relation supervenes 1997: 199].
The weaker principle would seem to obviate the need for propositions, which in this context deserve to be regarded with particular suspicion. We start with the idea that true assertions, statements, utterances, claims—representations generally—require truthmakers. Propositions stand as uneasy intermediaries between true representations and truthmakers, purely philosophical posits. We begin with one puzzle: how are truthmakers related to true utterances, beliefs, and the like. The answer: they make true propositions expressed by those utterances and claims. But now we have traded one puzzle for three puzzles: (1) how are truthmakers related to propositions; (2) how are propositions related to utterances and claims that ‘express’ them; (3) what is the nature of a proposition?
If we take up the idea that truthmaking is an internal relation between truths and truthmakers, the unattractiveness of an appeal to propositions becomes even clearer. Internal relations supervene on their relata: if you have the relata, you have the relation. You could put this less informatively by saying that internal relations are necessitated by their relata. This, it would seem, is the sense in which truthmakers necessitate truths.
Philosophers suspicious of truthmaking sometimes challenge those who find talk of truthmaking a useful philosophical concept to produce an informative accounting of the truthmaking relation. If truthmaking is an internal relation, however, it is unreasonable to expect such an account. It would be unreasonable in the same way that it would be unreasonable to insist on an informative account of the taller-than relation. What does require an accounting is the nature of intentionality or representation. If ever we could be clear on what representation is, we would have everything we need for an understanding of truthmaking.
Talk of representation might lead naturally back to thoughts of propositions. I have already suggested Armstrong's appeal to propositions creates more problems than it solves. Although I think there are many reasons to regard propositions as dodgy entities, let me mention just one here. Propositions, whatever else they are, have their meaning built in. Unlike ordinary inscriptions or utterances, propositions are representations that possess intrinsic significance. A proposition requires no interpretation, no deployment by intelligent agents. The proposition that snow is white is essentially that very proposition, a representation that snow is white that is essentially that very representation.
Armstrong expresses hope that we could work out a naturalistic account of propositions, but its hard to see how such an account would go. When we think of ordinary intentional items, we think of items the significance of which stems from their deployment. Signs, by themselves, linguistic or otherwise, are empty. They acquire significance by the uses to which they are put by intelligent agents or by intelligent systems generally. You need not have a worked-out theory of use to recognize that the intentionality of a representation could not be intrinsic to the representation.
Propositions are designed to have intrinsic, built-in intentionality. This looks, from the perspective of naturalistic theorizing, starkly magical. Although there is reason to be optimistic about the prospects of a naturalistic accounting of intentionality, the prospects for naturalizing propositions seem to be nil.
Propositions, no less than the totality state of affairs, have their roots in linguisticism. Inscriptions and utterances lack intrinsic meaning. Reflection on this point pushes us back to thoughts expressed by inscriptions and utterances. But thoughts, considered as states of representing agents, are no less bereft of intrinsic significance. We can halt what appears to be a threatening regress by positing propositions. We build into propositions just those elements missing from other forms of representation, a capacity for intrinsic meaning. Thoughts inherit the significance of the propositions they express and pass this significance along to thinkers' inscriptions and utterances.
Propositions can anchor accounts of intentionality because this is what they are posited to do. But this means that appeal to propositions in accounts of meaning resembles appealing to God to explain the nature of the world. Why is the world this way? Because God made it so. You will be satisfied by such an explanation only if you lack genuine curiosity. In the same way, appeals to propositions inhibit, rather than, encourage serious thought about intentionality and truth.
Linguisticism adieu
Commitments to totality facts and propositions, in their own ways, reflect the enduring influence of linguisticism. In engaging in semantic descent, in moving from talk about talk about the world, to talk about the world, we can lose our bearings and mistake features of descriptions of reality for reality itself. This, I have suggested, is the source of enthusiasm for the totality fact.
Similarly, the appeal of propositions, sentence-like entities with built-in representational powers, is rooted in the delusion that the world, or the world as we consider it, is a linguistic entity. The pull of this idea survives the demise of its philosophical credentials. We find in propositions what we cannot find in worldly sentences or representations generally. It is time we moved on. We know enough to know that sentences and representations acquire significance, not by standing in a special relation to other representations, sentences, or sentence-like entities, but by being put to use by intelligent systems. In this light, propositions reveal themselves as lingering category mistakes.
I see all this as fully in line with Armstrong's fiercely naturalistic approach to ontological questions. Armstrong has always appreciated that linguisticism represents a distraction from serious ontology. My recommendation is that we hold on to that thought and go all the way with it. Where ontology is concerned, the sooner we put the echoes of linguisticism behind us the better.
Notes
1Quoted in Armstrong Citation2004: 68] from Russell Citation1972: 93 – 4; see Citation1985: 103].
2‘Linguisticism’ used as it is used here originated, I believe, with C. B. Martin.
3See Heil Citation2000; Citation2003: chap. 7] for discussion.
4I follow Armstrong in using ‘fact’ and ‘state of affairs’ interchangeably: facts are states of affairs; states of affairs are instantiations of universals by substances (at times).
5Being a planet and being a state of affairs are ‘second-rate properties’ possessed by objects only by virtue of their possession of more respectable properties. Think of the property of being a planet, for instance, as whatever it is in virtue of which it is true that something is a planet.
6Armstrong addresses this worry in his 1997: 198 – 9] and again, in response to Cox Citation1997, in Armstrong Citation2004: 78 – 9].
7One possible response here would be to deny that the truthmaker for ‘p is true’ is identifiable with the truthmaker for p. We are supposing, after all, that p is a truth bearer, so the truthmaker for ‘p is true’ might be thought to include both the truth bearer, p, and p's truthmaker. Subsequent truths (that ‘p is true’ is true, for instance) might then be taken to supervene on the truth of ‘p is true’.
8Could there be a world lacking a totality fact? Armstrong suggests that the empty world might be such a world 2004: 75].
References
- Armstrong , D. M. 1997 . A World of States of Affairs , Cambridge : Cambridge University Press .
- Armstrong , D. M. 2004 . Truth and Truthmakers , Cambridge : Cambridge University Press .
- Bigelow , J. 1988 . The Reality of Numbers: A Physicalist's Philosophy of Mathematics , Oxford : Clarendon Press .
- Cox , D. 1997 . The Trouble with Truth-Makers . Pacific Philosophical Quarterly , 78 : 45 – 62 .
- Heil , J. 2000 . Truth Making and Entailment . Logique et Analyse , 169 – 70 : 231 – 242 .
- Heil , J. 2003 . From an Ontological Point of View , Oxford : Clarendon Press .
- Russell , B. 1919 . The Philosophy of Logical Atomism . Lectures 5 and 6, Monist , 29 : 190 – 222 .
- Russell , B. 1956 (1919) . “ The Philosophy of Logical Atomism, Lectures 5 and 6 ” . In Logic and Knowledge: Essays 1901 – 1950 , Edited by: Marsh , R. C. 175 – 281 . New York : G. P. Putnam's Sons .
- Russell , B. 1972 (1919) . Russell's Logical Atomism , Edited by: Pears , D. London : Fontana .
- Russell , B. 1985 . “ The Philosophy of Logical Atomism, Lectures 5 and 6 ” . In The Philosophy of Logical Atomism , Edited by: Pears , D. 35 – 155 . LaSalle, IL : Open Court .