Plenitudinous Russellianism, ‘That’-Clauses, and the Principle of Substitutivity

ABSTRACT Recently, in a series of papers, Joshua Spencer has introduced, defended, and developed a modified version of Neo-Russellianism (NR), namely Plenitudinous Russellianism (PR), according to which there are structurally identical but numerically distinct singular Russellian propositions (SRPs). PR claims to provide novel semantic solutions to all the major problems that NR faces with no radical revision in NR. In this paper, I introduce a semantic puzzle for PR: the view leads to the violation of the principle of substitutivity of co-referential proper names within simple (predicative) ‘that’-clauses (PS1). I consider different responses to my argument, and show that none of them is fully satisfactory for the Russellian. I conclude that PR needs to depart from NR more radically.

Kaplan’s Counterexample to Quine’s Theorem

In his article “Opacity” (1986), David Kaplan propounded a counterexample to the thesis, defended by Quine and known as Quine’s Theorem, that establishes the illegitimacy of quantifying from outside into a position not open to substitution. He ingeniously built his counterexample using Quine’s own philosophical material and novel devices, arc quotes and $entences. The present article offers detailed analysis and critical discussion of Kaplan’s counterexample and proposes a reasonable reformulation of Quine’s Theorem that bypasses both this counterexample and another, in the author’s opinion, more persuasive counterexample, also discussed in this paper and somehow implicit in “Opacity”, which involves Russellian propositions instead of the Quinean apparatus.

Numbers, Reference and Russellian Propositions

Stewart Shapiro and John Myhill tried to reproduce some features of the intuitionistic mathematics within certain formal intensional theories of classical mathematics. Basically they introduced a knowledge operator and restricted the ways of referring to numbers and to finite hereditary sets. The restrictions are very interesting, both because they allow us to keep substitutivity of identicals notwithstanding the presence of an epistemic operator and, especially, because such restrictions allow us to see, by contrast, which ways of reference are not compatible with the simultaneous maintenance of substitutivity of identicals and the classical notions of truth and knowledge. In this paper the difference between the restricted and the unrestricted kind of reference is put in relation with Russell's ideas on naming and it is argued that the latter as well is compatible with a certain Russellian conception of the understanding of sentences. Then it is discussed whether and how numbers could be conceived as objects of acquaintance. Finally a general question about the notion of logical form is raised.