Abstract
William Child (2002) has argued that one cannot tenably hold the middle ground between constructivism and platonism. In this paper, I will argue that by relying on Stroud’s notion of ‘naturalness’, a common-sense realist position can be maintained that avoids the excesses of constructivism and the paradoxes of platonism.
Table of contents
William Child (2002) argues that one cannot tenably hold the middle ground between constructivism and platonism. In this paper, I will argue that by relying on Stroud’s notion of ‘naturalness’, a common-sense realist position can be maintained that avoids Child’s objection. Although Child himself is somewhat sympathetic with common-sense realism, he is unable to fully endorse the view as he sees it as leaving unanswered one particularly pernicious worry. He asks:
[W]hat makes it the case that someone has grasped just this rule, with these investigation-independent standards of correctness? In particular, how is that question to be answered in a way that neither tacitly endorses the platonist idea that certain rules are objectively simpler than others nor gives up the idea of investigation-independence and lapses into constructivism? (92-93, emphasis original)
Wittgenstein tells us that it is always possible for someone to seemingly follow one rule when, in fact, he has been following a different rule, with different standards of correctness, the entire time (e.g., his odd adder in PI §185). Given this possibility, how are we to differentiate between erring and following another rule? The platonist can solve this worry by appealing to the notion of a rule being “objectively simpler”, that there is a default or ‘obvious’ way to continue the series (Child, 191-92). The common-sense realist cannot invoke any equivalent idea because “any way of continuing a series can count as going on in the same way as before,” (192, original emphasis). Unfortunately, we cannot argue that the technique the adder was taught will provide the answer as the premise of Child’s objection is that we are uncertain which technique he is following. Because no feature of his behaviour will illuminate that question, we are consequently unable to claim that we know what his correct answers will be if he has not yet reached them.
Although the realist is apparently thwarted by this criticism, the constructivist is not. She can appeal to what the adder will do: the correct answer is available only when the rule follower performs the calculation in question, although even then we are unable to claim we have determined which rule he is following as his future actions may diverge from another rule follower’s (Child, 192). This response is clearly unacceptable to both the platonist and the common-sense realist as it abandons the conception of ratification-independence, but if Child is right, the realist has no response, even though she remains convinced that there is a correct answer regarding how an addition series is to be completed after, say, 2000 or 3000. Yet, if the realist cannot appeal to a platonic idea of simplicity and cannot endorse the constructivist’s view, how is she to proceed?
1. Stroud’s Response
In “Wittgenstein and Logical Necessity,” Stroud defends Wittgenstein from Dummett’s constructivist interpretation. Although the issues with which Stroud is concerned are not precisely those of Child’s, the lesson he draws should prove useful. Dummett’s conclusion that Wittgenstein is a constructivist rests upon passages (e.g., the wood-sellers or the odd adder) that tell us it is possible for someone to perform calculations identical to those that we make, but also to continue on in radically different ways than we would expect. For Dummett’s Wittgenstein, there is nothing in the rules that forces us to continue on in any way other than “our having expressly decided to treat that very [rule] as unassailable” (p. 329). Such a position is clearly at odds with platonism and so Dummett concludes that Wittgenstein must be endorsing a constructivist account of rule following.
Stroud, however, rejects this interpretation of Wittgenstein. For Stroud, the notion of ‘force’ that Wittgenstein is criticizing is the platonic one of rails to infinity that guide our actions without our involvement, not a disavowal of ratification-independent standards of correctness. Accordingly, he surmises that Dummett has misread Wittgenstein’s examples of calculating differently as mistaking an attack on platonism for a positive argument for constructivism. Stroud’s project continues in the hopes of explaining “what makes the denial of a necessary truth ‘impossible’ or ‘unintelligible’” (504) without invoking a platonic idea of truth or obviousness. It is my contention that this idea will prove useful not just in providing a common-sense realist interpretation of Wittgenstein, but also in making possible a means of defense against Child’s criticism.
Stroud stresses that many of Wittgenstein’s examples used by the constructivists are dead choices. Once we investigate the consequences of behaving in the way that the examples suggest, outside of their isolated contexts, we quickly understand how truly unintelligible they are (Stroud, 512). If we are to treat, for example, the wood-sellers as genuinely intelligible, we must consider how they understand the world and see if it is comprehensible. The wood-sellers, if their system is a coherent one, must also believe that carpenters use the same amount of wood in building a small, but extraordinarily tall house as when they build a house equal in area, but quite short, and this really is quite strange.
But what accounts for this strangeness? For Stroud, intelligibility stems from our common agreements and judgments, our form of life. But this agreement is not of the sort to which we could consciously decide to adhere or refute, but a constitutive fact about us that stems from the history of our species -- the biological, physiological and psychological facts of our evolution (Stroud, 514). Importantly, this is not an invocation of a platonic conception of agreement or rule following. What we consider natural ways of rule following might well have been otherwise if our historical development had been different. As a result, what we would consider intelligible would also change. While what we deem natural remains a contingent fact, this is commensurable with ratification-independence and requires no endorsement of a constructivist reading of Wittgenstein.
Moreover, “there are rails that we have already traveled, and we can extend them beyond their present point only by depending on those that already exist. For the rails to be navigable they must be extended in smooth and natural ways…” (Stroud, 518). What we consider to be “smooth and natural” is a result of our shared judgements, the bedrock we must have in common in order to communicate and be mutually intelligible. Yet Stroud (and through him, Wittgenstein) is emphatic in distinguishing this sense of ‘natural’ from a platonic conception (Cf. Stroud, 517-518 and Wittgenstein, PI §241). Stroud does not allow for rules to exist ‘outside’ of us, nor are the ways we follow rules constructed. The extension of the rails is constrained by our shared judgements of what we consider to be intelligible and this is not open to alteration in the way the constructivist allows. By staking out this middle ground, Stroud provides an interpretation of objectivity without platonic overtones that is well-suited to common-sense realism.
Nevertheless, Child’s concern that we cannot distinguish between a person following this rule or that rule cannot be outright dismissed, but we can say that the weight he attributes to it is overly strong. He is right to claim that the common-sense realist must concede that it is always possible to follow an individual rule in a different way. However, it just so happens that the likelihood of us ever only following one rule in isolation from all others is so remote as to not pose a serious problem for anyone but the most sceptical of sceptics (and it seems his worries are largely unintelligible). Furthermore, if Stroud is right in reading Wittgenstein’s examples as directed against platonism and not in favour of full-blown constructivism, the crux of Child’s argument is stolen from him. The examples of the wood-sellers, etc. do not point the way towards a constructivist program, but ward against platonism. To interpret them otherwise is to misread Wittgenstein, a claim that Child has lodged against the common-sense realist. Still, we must defend Stroud’s account of intelligibility before we can feel secure that we have answered Child’s worries.
2. Bloor’s Critique
One might worry that Stroud’s conception of naturalness is too close to the idea of simplicity used by platonists. This concern is raised by Bloor (1997) who views Stroud’s invocation of ‘naturalness’ as a hackneyed attempt to refute constructivism. While Bloor is correct to reinforce the point that our biological predispositions cannot tell us how social institutions, languages, etc. will unfold, he seems to be missing the deeper point of Stroud’s use of ‘natural’. It is important to clarify what Stroud is not claiming: he is not suggesting that different mathematical systems are impossible, or even that some might be contradictory, but that the way we follow rules, not what those rules are, is not up for discussion. What Stroud is after is an account of intelligibility -- what makes something understandable or otherwise -- and provides it without claiming, as Bloor suggests, that our cultural institutions are in any way inevitable or that all alternatives are unthinkable.
Thus, Stroud is certainly not asserting that the systems we use to measure the world are in any way obvious or determined, nor would he disagree that they are historically contingent. He is asserting that someone who understands and equates the rule ‘+2 forever’ with ‘+6 after 2000’ is not differing just in systems of measurement, but engaging in a truly incomprehensible (for us) system of rule following. Therefore, Bloor’s parallel between the differences in Euclidian or Einsteinian mathematics is largely irrelevant. The systems may differ in how they profess to understand the world, but their shared bedrock of rule following is similar. Einsteinian mathematics may see space as curved while for the Euclidian it is infinitely flat, but neither system suggests that ‘+2’ could coherently entail ‘+6 after 2000’, or that someone wouldn’t be quite idiosyncratic in making that leap. So, Bloor has attacked a strawman; must a Euclidian system have been the inevitable outcome of our biology and psychology? Of course not, but Stroud never made such a claim. The concept of ‘natural’ that Stroud discusses is quite specific and shares only a superficial resemblance to the view criticized by Bloor.
Moreover, as Bloor presupposes that different culturally determined institutions are intelligible, he must supply an account of that intelligibility. While his examples of Euclidean and Einsteinian mathematics do differ, they remain (with some training) understandable. Yet, it is not clear that Bloor has a theory of this intelligibility available to him without biting the bullet and giving a fuller account of what our bedrock agreements are and what they consist in. If cultural practices can remould our instincts and our pre-theoretical conceptions of intelligibility (and Bloor seems very close to saying exactly this), then we should be unable to experience cross-cultural intelligibility as cultures will have changed and, over time, become mutually or partially incomprehensible. But this is not the case. It may not be easy to understand another culture, but that is not to say it is impossible to do so. Unless Bloor provides an explanation of this intelligibility or denies it altogether, we can dismiss his criticism of Stroud and refocus on Stroud’s account of intelligibility stemming from our shared form of life.
That is, there is some common ground that humanity shares, untouched by cultural forces. The manner in which we build on those similarities will differ according to our culture, history, etc., but we cannot alter the building blocks themselves without becoming incoherent. That Stroud lacks a detailed account of exactly what those human similarities are is frustrating (although his examples of coherency and intelligibility in rule following are illuminating), but not crippling to the defense of common-sense realism. Through the exploration of Stroud and Bloor, we are equipped with the tools needed to answer Child’s objection to common-sense realism.
To briefly summarize, the lessons that Stroud has taught us are threefold. First, we must remember that Wittgenstein’s examples were created to distill the incoherency of the platonist’s account of rule following, not to endorse constructivism. Second, the examples were of single instances of rule following used to argue the first point; understood holistically as Stroud suggests, their unintelligibility becomes apparent. And third, there must be common bedrock elements of human psychology and biology that set the parameters for our understanding. These parameters must account for the ‘natural’ way we follow rules. Combined, these three are more than sufficient to answer Child’s objection. Consequently, his charge that the common-sense realist is without the ability to distinguish between a person following this rule or that rule without a) appealing to what he will do in the future as a constructivist would do, or b) invoking the platonic notion of simplicity, is shown to be a false choice.
Indeed, with Stroud’s account of intelligibility properly deployed, Child has far less room to suggest that “any way of continuing a series can count as going on in the same way as before,” (p. 192, original emphasis). Instead, we can allow for non-platonic constraints on the way we follow rules that are built upon our common human nature and common features of the world. Additionally, once we recognize that Wittgenstein’s examples are isolates used to argue against platonism and any attempt to raise a coherent and holistic system on those examples is doomed, we see Child’s constructivist interpretation of Wittgenstein as being largely flawed. As a result, Child’s worry is correctly diagnosed as stemming from an overly constructivist reading of Wittgenstein’s program and can be safely shelved. This supplies the common-sense realist the response she needs to retain ratification-independent standards of correctness and an objective, non-platonic way of answering Child’s sceptical charge. Although not above all criticism, such a response is, at the very least, a promising place to begin.
Literature
- Bloor, David. 1997. Wittgenstein, Rules and Institutions. New York: Routledge.
- Child, William. 2002. Wittgenstein and Common-Sense Realism. Facta Philosophica, 2, 179-202.
- Dumment, Michael. 1959. Wittgenstein's Philosophy of Mathematics. Philosophical Review, 68, 324-348.
- McDowell, John. 2002. Wittgenstein on Following a Rule. In A. Miller & C. Wright (Eds.), Rule-Following and Meaning. Montreal: McGill-Queen's University Press.
- Stroud, Barry. 1965. Wittgenstein and Logical Necessity. Philosophical Review, 74, 504-518.
- Wittgenstein, Ludwig. 1961. Tractatus Logico-Philosophicus (D. F. Pears & B. F. McGuiness, Trans.). London: Routledge.
- Wittgenstein, Ludwig. 1978. Remarks on the Foundations of Mathematics (G. E. M. Anscombe, Trans.) Oxford: Blackwell.
- Wittgenstein, Ludwig. 2001. Philosophical Investigations (G. E. M. Anscombe, Trans. Third ed.). Oxford: Blackwell.
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