Closed Structure

According to the structured theory of propositions, if two sentences express the same proposition, then they have the same syntactic structure, with corresponding syntactic constituents expressing the same entities. A number of philosophers have recently focused attention on a powerful argument against this theory, based on a result by Bertrand Russell, which shows that the theory of structured propositions is inconsistent in higher order-logic. This paper explores a response to this argument, which involves restricting the scope of the claim that propositions are structured, so that it does not hold for all propositions whatsoever, but only for those which are expressible using closed sentences of a given formal language. We call this restricted principle Closed Structure, and show that it is consistent in classical higher-order logic. As a schematic principle, the strength of Closed Structure is dependent on the chosen language. For its consistency to be philosophically significant, it also needs to be consistent in every extension of the language which the theorist of structured propositions is apt to accept. But, we go on to show, Closed Structure is in fact inconsistent in a very natural extension of the standard language of higher-order logic, which adds resources for plural talk of propositions. We conclude that this particular strategy of restricting the scope of the claim that propositions are structured is not a compelling response to the argument based on Russell’s result, though we note that for some applications, for instance to propositional attitudes, a restricted thesis in the vicinity may hold some promise.

The Functional Composition of Sense

A central dispute in understanding Frege’s philosophy concerns how the sense of a complex expression relates to the senses of its component expressions. According to one reading, the sense of a complex expression is a whole built from the senses of the component expressions. On this interpretation, Frege is an early proponent of structured propositions. A rival reading says that senses compose by functional application: the sense of a complex expression is the value of the function denoted by its functional component for the arguments denoted by its remaining components. I argue that two non-negotiable Fregean theses entail that senses compose by functional application. One thesis is that referents compose by functional application. The other thesis is that an expression in an indirect context refers to its customary sense.

First among equals: co-hyperintensionality for structured propositions

Theories of structured meanings are designed to generate fine-grained meanings, but they are also liable to overgenerate structures, thus drawing structural distinctions without a semantic difference. I recommend the proliferation of very fine-grained structures, so that we are able to draw any semantic distinctions we think we might need. But, in order to contain overgeneration, I argue we should insert some degree of individuation between logical equivalence and structural identity based on structural isomorphism. The idea amounts to forming an equivalence class of different structures according to one or more formal criteria and designating a privileged element as a representative of all the elements, i.e., a first among equals. The proposed method helps us to a cluster of notions of co-hyperintensionality. As a test case, I consider a recent objection levelled against the act theory of structured propositions. I also respond to an objection against my methodology.

Propositions as (non-linguistic) objects and philosophy of law: Norms-as-propositions

The paper distinguishes two accounts of legal normativity. One-source accounts claim there is only one source for legal normativity, which is ultimately linguistic. Two-source accounts claim legal normativity is both linguistic and non-linguistic. Two-source accounts claim we need to go beyond language and beyond propositions taken as linguistic entities, while they are one-source accounts? main conceptual tool. Both accounts construct propositions as linguistic. There is, nevertheless, a documented analytic tradition starting with G.E. Moore that constructs propositions as non-linguistic entities. Today, the problem of the unity of proposition and structured propositions are highly debated in metaphysics. How does such debates fit into the one-source vs. two-source picture of legal normativity? Why has analytic legal philosophy failed to consider such an option concerning propositions (arguably calling descriptive sentences about norms ?normative propositions? did not help)? This paper thus (I) reconstructs the argumentative dynamics between one-source and two-source accounts; (II) presents the less considered philosophical view of propositions as non-linguistic entities and (III) discusses how to include or dismiss such a philosophical view in the one-source/two-source debate on legal normativity.