How many truth-values are there? Although this appears to be a very simple question, in my opinion it defies any very simple answer. Some of us have trouble making up our minds. Frege, who invented the term “truth-value”, declared that apart from Truth and Falsity “there are no further truth-values”; and yet Frege, who introduced many of us to semantic presuppositions, acknowledged truth-value gaps. Now how many values would that be? On one way of counting, True, False and Gap make three. To be sure it's not Frege's way of counting; but it's defensible. And we are left with the historical puzzle that Frege, who founded his semantics on the insistence that functions be everywhere defined—without any gaps—has come to be known as the author of the doctrine of semantic presuppositions and truth-value gaps.

For a very long time truth-value gaps were under a cloud of suspicion because they were considered logically unmanageable. So Frege declared that:

Three-valued logic promised to dispel the cloud but in the eyes of many it had promised more than it could deliver. So in response to Reichenbach's plea for a three-valued quantum logic Russell replied:

‘By now technical skill has supplied many alternative systems of three-valued logic, but few answers and numerous additional difficulties.’

This paper has two parts. In part I, I review two older accounts of the logical forms of modifiers (adjectives, adverbs and prepositional phrases), and suggest that they may be combined with each other so as to yield a theory that is better than either of its parts taken singly. Part of this theory involves the idea that certain sentences refer to events, states, or processes; Part II of this paper shows how to use this idea to account for tenses and temporal adverbials, and offers a new account of ordinary language quantification.

In this discussion I take it for granted that proper names are words of a language, are not mere interjections or burps. I also take it for granted that for any proper name “N. N.” there is some general term “A” that gives the relevant criterion of identity; repeated use of “N. N.” involves an intention to keep on saying things about one and the same A, or as I shall put it for short “N. N.” is a name for an A. An intention to keep on referring barely to the same thing is, as lawyers say, void for uncertainty. (A name for an A may or may not be a name of an A; it will not be a name of an A if through some mistake or fraud or again confusion of two A's together, the name “N. N.” gets used without assignable reference.)

These theses have been denied, but I think not reasonably. Some very silly arguments have been used recently: e.g. an argument from the logical possibility of Protean change is put up to show that a proper name may attach to a thing no matter what sort it comes to belong to.

As interest in the study of natural languages has increased, philosophers of language and logicians have, along with linguists, begun to pay more attention to sentences whose truth value varies from context to context. Alternatively, to sentences which are such that, if different speakers utter them, those speakers may (or sometimes must) say different things. For example, it is well-known that two different people who utter ‘I am hot’ will be saying different things, that two different people who utter ‘Billy is a lush’ may be saying different things, and that different speakers who utter ‘The book on the table is boring’ may say different things. The same sort of familiar point could be made by examples concerning other pronouns, demonstratives, the utterance of ambiguous sentences, and so on.

In “Naming and Necessity” Saul Kripke repeatedly uses modal arguments to show that proper names are not abbreviated or disguised descriptions. The arguments take the following form:

1. (a) “The F might not have been the F” is false.

2. (b) If N were used to mean the F, then “N might not have been the F” would be false (because of (a)).

3. (c) But “N might not have been the F” is true.

4. (d) Therefore, N is not used to mean the F.

The numerous difficulties facing the traditional Humean regularity approach to the problem of causation have been discussed in the literature at great length. In view of the current interest in possible worlds semantics, it is not surprising that the only serious alternative treatment of causation presently available, the counterfactual approach, has been explored recently as a means of circumventing the apparently unresolvable difficulties facing regularity causal theories. It is the purpose of this paper to suggest that such a strategy holds little promise. Specifically, I will argue that, in addition to giving rise to problems directly analogous to those facing regularity accounts, the counterfactual approach fails in principle to reflect important properties of causal relations as we understand them intuitively. David Lewis's possible worlds account, the most comprehensive counterfactual theory to date, is further criticized for implicit problems with natural lawhood even more serious than those typically raised for regularity accounts, for additional inadequacies in its analysis of causal relations, and for its failure to satisfy basic empiricist epistemological standards.

Roughly speaking, references (as they concern us here) relate what is said to just those things about which it is said. A theory of reference is commonly taken to be a statement or characterization of that relation which references effect — that relation, that is, which holds between something that is said and some object just in case in that which is said (or perhaps in saying it) reference is made to that object. Such a theory is often further conceived as answering one or both of the questions: (a) For any given object X, what is it for a reference to be made to X (or under what conditions will a reference have been made to X?), and (b) For any given reference, R, what is it for an object X to be the referent of R (or under what conditions will X be the referent of R?). Let us call a theory which correctly answers at least some of these questions a classical theory of reference.

By a ‘semantic determinant’ I will mean“…a structural feature of the world necessary for the determination of truth and falsity …,” or briefly, “Semantic determinants are things that determine valuations.” (Thomason (1972), pp. 301, 302), where such determination is functional and where valuations are themselves functions from sentences into truth values. A familar example is the ‘domain of individuals’ relative to which truth conditions are given for sentences containing “all,” “some,” and related expressions, where these can be construed as ‘quantifiers.’ Thus, e.g., “Some men are albinos” is true just in case at least one individual in the domain which is a man is also an albino. For this truth condition to be making a definite claim we must suppose that the domain is a definite (though not necessarily finite) set of individuals fixed in advance.

As if we had in mind something like a scale of might-have-beens, erratically decreasing in specificity, in which each point provides some or all of the grounds for a transition to the next one, but not conversely, we could claim that Kleist might not have met Henriette Vogel; that he might not have committed suicide at all; that he might have had different properties than the properties he in fact had; even, in a somewhat figurative vein, that he might have been a different person than the person he was; and so on; and so forth, either adding new marks to the scale, or with a different scale in mind, along similar lines. Scales of this sort not only qualify as a kind of string of causally and temporally related might-have-beens; they also qualify, at the same time, as partial lists of true de re modal predications about Kleist.