Nuel Belnap

(? - 2024)

This paper offers a lighthearted presentation of some of the chief ideas about truth that are shared by theories similar to those of Kripke, Herzberger, and Gupta. The problem is to explain the concept of truth for a language that contains its own truth predicate. The proposal of these theories is that one can unwind the tangles that threaten by invoking a transfinite series of stages of semantic reflection as one ascends the ordinals. The presentation emphasizes how each stage begins, to the extent that it can, with the fruits of semantic reflection at earlier stages. Special attention is given to clarifying how these theories about truth treat the three chief kinds of ordinal numbers: the initial ordinal, successor ordinals, and limit ordinals.

There is no EPR-like funny business if (contrary to apparent fact)our world is as indeterministic as you wish, but is free from theEPR-like quantum mechanical phenomena such as is sometimes described interms of superluminal causation or correlation between distant events.The theory of branching space-times can be used to sharpen thetheoretical dichotomy between EPR-like funny business and noEPR-like funny business. Belnap (2002) offered two analyses of thedichotomy, and proved them equivalent. This essay adds two more, bothconnected with Reichenbachs principle of the common cause, theprinciple that sends us hunting for a common-causal explanation ofdistant correlations. The two previous ideas of funny business and thetwo ideas introduced in this essay are proved to be all equivalent,which increases ones confidence in the stability of (and helpfulnessof) the BST analysis of the dichotomy between EPR-like funny businessand its absence.

We are grateful to Professor Robert Koons for his excellent, and generous, review (henceforth KR) of our book The Revision Theory of Truth (henceforth RTT). Koons provides in KR a welcome guide to our RTT, and he puts forward objections that deserve serious consideration. In this note we shall respond only to his principal objection.' This objection, which is developed on pp. 625 — 628 of KR, calls into question our main thesis. As we argue below, however, the objection is not successful. We should forewarn the reader that this note is not self-contained. It presupposes familiarity with RTT (primarily, Chapter 4) and with KR. The main thesis of RTT is that truth is a circular concept. We argued that the Tarski biconditionals, read as partial definitions, constitute an intensionally adequate definition of truth. In other words, if T is a predicate defined by the Tarski-style infinitistic definition (I).