Truth, Consequence and the Universality of Reason – Michael P Lynch

Lynch writes from the perspective of an alethic functionalist, that is ‘truth is a functional property that can be realised…in more than one way…If truth were a functional property, then our true beliefs about the concrete physical world needn’t manifest truth – or “be true in the same way” – as our thoughts about matters where the human stain is deepest, such as morality or the law’ (3). So defined, truth is an immanent property. This core truism about truth allows us to retain the intuition that truth is one, as well as saying that the ways in which it is manifested can be many. That is, functionalism entails pluralism about truth.

In this chapter, Lynch is concerned with the consequences of the pluralistic definition of truth in terms of its relation to different domains of reason or inquiry. Though analysis of the truth property in atomic propositions appears, superficially at least, to be reasonably straightforward (p is true if and only if p is true), compound propositions – and mixed compounds in particular – present a set of problems for the alethic functionalist.

Mixed compounds are demonstrated by propositions such as ‘murder is wrong and the book is on the table’. The problem points to a deeper concern than a merely technical issue; specifically, how do we reason across different domains of inquiry? For if what is true varies across different domains – from the moral to the physical in the example above – then how can reason be universally applicable in different domains? We could potentially wind up with as many ways of reasoning as there are propositions.

One strategy in the case of mixed compounds stems from the definition of mixed inferences: ‘a valid inference is one where truth is preserved across its manifestations from the premises of the argument to its conclusion’. Analogously, The recursive strategy would apply the theory in the first instance to atomic propositions, and then understand compound propositions as ‘a truth-function of the atomic proposition of which it is composed’. But does this mean that compound propositions have a truth of their own or not? For the functionalist, compound propositions are true without manifesting truth. They thereby follow thinkers like Russell and Wittgenstein, who claimed that logical constraints do not manifest [themselves].

Thus, compound propositions are only true in a derivative sense. This claim accords with another Wittgensteinian intuition that the only thing that makes a compound true is the truth of its component parts. Moreover, the functionalist view parallels truth-maker theories, which similarly hold that there are no compound truth-makers. There are costs involved with holding this view, however; Lynch argues that holding the extensional definition of the truth disjunctive requires us to revise the original theory. The original theory looked something like this:

For all propositions P, P is true if and only if it has a property that manifests truth.

This must now be replaced with the following characterisation:

A proposition is true iff it manifests truth or is a derivatively true truth-functional compound proposition.

Thus, the property of truth can either be held or derived, leading to the claim that it can be manifest in more than one way, described below in relation to domain-specific logical pluralism.

Lynch doesn’t think that replacing the original theory with the above characterisation is a problem. The functionalist can adopt a weak grounding principle to show how compounds supervene on the atomic; the principle holds that there can be no change in the truth-value of some atomic proposition. Furthermore, manifestation, as a reflexive relation, allows the functionalist to say that ‘when a proposition is true only by virtue of self-manifesting truth, we can say that the relevant proposition is plainly true’. That is, a compound proposition is plainly true if their truth-value is grounded. This view is amenable to the functionalist because she is already committed a) the thought that what’s true depends on what is true in a particular way, and b) via her account of propositional domains, to the idea that true atomic propositions have further properties like superwarrant, which manifest truth.

We now come round to what seems to be Lynch’s principle concern, namely, the problem of logical pluralism and whether the functionalist is committed to this view. Logical pluralism is the view that there is more than one logic governing our reasoning. It therefore begs the question is there more than one way for an argument to be valid?

Beall and Restall are two contemporary logical pluralists. They put forward the claim that an argument is valid if and only if, in every case where the premises are true, so is the conclusion. This minimal concept of truth, they argue, can be further enriched, but only if the enrichment stems from additions that are necessary, normative or formal. Thus the classical and constructivist formulations:

Classical: An argument is valid if and only if in every possible world where the premises are true, so is the conclusion

Constructivist: An argument is valid if and only if at every possible stage of inquiry where the premises are true, so is the conclusion.

The latter formulation is similar to the functionalist’s account of superwarrant, whereby stages of inquiry are both extensible (additional information might always come in) and inclusive (all successive stages of inquiry include the information warranted at previous stages).

Domain specific logical pluralism (DLP) holds that the classical formulation might apply in some cases, and the constructivist might apply in others. Lynch is quick to point out that there is no direct route from functionalism about truth to DLP: just because there is more than one way for a proposition to be true does not mean that there must be more than one way for truth to be preserved from one proposition to another. There could, however, be an indirect link, for if there is more than one way to manifest truth, and some of the manifesting properties are epistemically defined properties like super warrant, and some not, then different domains will admit of different manifestations of the consequence relation. That is, some argument forms are valid in some domains and not others. Nonetheless, Lynch argues that the functionalist is still not committed to DLP, for she can either deny that truth is variably manifested or claim that our truisms about truth constrain the logic that governs any given domain. In spite of the get out clause provided, Lynch claims that the functionalist will probably still allow for some version of DLP, but she would ‘do well to be modest’, and claim:

Modest: where a compound proposition or inference contains propositions from distinct domains, the default governing logic is that comprised by the intersection of the domain-specific logics in play.