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Two different uses of ‘proposition’ are distinguished: the meaning of an eternal sentence is distinguished from that which can be asserted, believed, conjectured, and so on. It is argued that, in the second sense of ‘proposition’, it is not the case that every proposition can be expressed by an eternal sentence.

Logic begins but does not end with the study of truth and falsity. Within truth there are the modes of truth, ways of being true: necessary truth and contingent truth. When a proposition is true, we may ask whether it could have been false. If so, then it is contingently true. If not, then it is necessarily true; it must be true; it could not have been false. Falsity has modes as well: a false proposition that could not have been true is impossible or necessarily false; one that could have been true is merely contingently false. The proposition that some humans are over seven feet tall is contingently true; the proposition that all humans over seven feet tall are over six feet tall is necessarily true; the proposition that some humans are over seven feet tall and under six feet tall is impossible, and the proposition that some humans are over nine feet tall is contingently false. Of these four modes of truth, let us focus on necessity, plus a fifth: possibility. A proposition is possible if it is or could have been true; hence propositions that are either necessarily true, contingently true, or contingently false are possible. Notions that are similar to the modes of truth in being concerned with what might have been are called modal. Dispositions are modal notions, for example the disposition of fragility. Relatedly, there are counterfactual conditionals, for example “if this glass were dropped, it would break.” And the notion of supervenience is modal.1 But let us focus here on necessity and possibility. Modal words are notoriously ambiguous (or at least context-sensitive2). I may reply to an invitation to give a talk in England by saying “I can’t come; I have to give a talk in California the day before”. This use of “can’t” is perfectly appropriate. But it would be equally appropriate for me to say that I could cancel my talk in California (although that would be rude) and give the talk in England instead. What I cannot do is give both talks..

Over a period of more than twenty years, Sybil Wolfram gave lectures at Oxford University on Philosophical Logic, a major component of most of the undergraduate degree programmes. She herself had been introduced to the subject by Peter Strawson, and saw herself as working very much within the Strawsonian tradition. Central to this tradition, which began with Strawson's seminal attack on Russell's theory of descriptions in ‘On Referring' (1950), is the distinction between a sentence and what is said by a sentence − Strawson initially called the latter a use of a sentence, and sometimes a proposition , but his most frequent term for what is said , which Wolfram consistently adopts, is the statement expressed.1 The force of the distinction is clearly illustrated in ‘On Referring', which uses it to undermine the common assumption that any sentence must be either true, or false, or meaningless. Russell had argued on this basis that a sentence such as ‘The King of France is bald' (which is clearly neither true nor meaningless) must be false, but Strawson points out that if we distinguish between the sentence itself and the statement that it expresses (on some occasion of use), we can quite easily combine the admission that the sentence is meaningful − for it can in appropriate circumstances be used to express true and false statements − with the claim that nevertheless if the circumstances are ‘inappropriate' (in particular, when there is no current King of France), the sentence can fail to express a statement that is either true or false. On this picture, therefore, it is sentences that are meaningful, but statements that are the primary bearers of truth.

Probabilities range from 0 to 1. If a proposition has a probability of 0, then it’s certainly false; if 1, then it’s certainly true. A proposition with a probability of ½ (or 0.5, or 50%) is equally likely to be true as false, and a proposition with a probability of ¾ (or 0.75, or 75%) is three times as likely to be true as false.

When I assertively utter the sentence `Spot is a cat', the sentence I utter expresses a proposition. The truth condition of the proposition so expressed is determined by the semantic values of the singular term, `Spot', and the predicate, `is a cat'. If `Spot' refers to a certain particular entity E and `is a cat' expresses a certain particular property P, then the proposition in question is true if and only if E has P. Such is the theoretical cash value of reference. The referent of a given singular term generally figures in this manner in the truth condition of the proposition expressed by any sentence containing the singular term outside direct quotations and other referentially opaque contexts.1 Given this understanding of the notion of reference, I wish to address an important question: How is the reference of a proper name determined?

“To this day, partiality approaches to the paradox have been dogged by the so-called ‘Strengthened Liar’. .... The Strengthened Liar observes that if we follow a partiality theorist and declare the Liar sentence* neither true nor false (or failing to express a proposition,. or suffering from some sort of grave semantic defect), then the paradox is only pushed back. For we can go on to conclude that whatever this status may be, it implies that the Liar sentence is not true. This claim is true, but it is just the Liar sentence again.* We are back in paradox.” (Glanzberg 2002, p. 468, bold emphasis added.) Cf.: “We are back in our contradiction,”(Glanzberg 2001, p. 222). *The Liar sentence intended is evidently the sentence ‘the Liar sentence is not true’, and, the Liar sentence = ‘the Liar sentence is not true’. Cf.: “Consider a Liar sentence: ...let us take a sentence l which says l is not true. We can, informally, reason as..

(1) I’m Spartacus! [Said by Spartacus] (2) I’m Spartacus! [Said by Antoninus] What Spartacus said was true, and what Antoninus said was not. Yet the two slaves uttered the exact same sentence, so how can this be? Admittedly, the puzzle is not very hard, and its solution is uncontroversial. The first person pronoun “I” is – to use a technical term – context sensitive. When Spartacus uses it, it refers to Spartacus; when Antoninus uses it, it refers to Antoninus. So when Spartacus says “I’m Spartacus”, he expresses the true proposition that he, Spartacus, is Spartacus. And when Antoninus says it, he expresses the false proposition that he, Antoninus, is Spartacus. The sentence “I’m Spartacus” expresses different propositions when used by different people. Another example will help. Contrast these two utterances, made by subjects in a study carried out by experimental epistemologists: (3) This is a zebra. [Said by someone while pointing at a zebra] (4) This is a zebra. [Said by someone while pointing at a cleverly decorated mule].

The status of premise 1 is controversial: friends of two dimensional modal logic (and others) will be reluctant to grant that the proposition that I exist is both contingent and knowable a priori (even by me). Instead, they will insist that all that I know a priori is that the sentence "I exist" expresses some true proposition or other when I token it. But, of course, even that will suffice for the purposes of the argument. Provided that I know a priori that the sentence "I exist" expresses some true singular proposition or other -i.e. some proposition or other which contains an individual -then I have an a priori guarantee that there are some individuals, and so I am entitled to assert 2. Of course, it will remain true that there are some people who refuse to accept 2: consider, for example, those ontological nihilists who think that the proper logical form of every sentence can be given in a feature placing language. [3] However, many people will be prepared to grant that we can know a priori that there are at least some individuals -and that it enough to sustain interest in our argument to this point.

I argue here that Frege’s eventual view on the relation between sentences and the thoughts they express is that, ideally, a sentence expresses exactly one thought, and a thought is expressed by exactly one (canonical) sentence. This may clash with some mainstream views of Frege, for it has the consequence of de-emphasizing the philosophical significance of the question of how it is possible for someone to regard one sentence as true yet regard another sentence that expresses the same thought as false. This account of Frege was developed by taking a long-range look at his writings over the course of his life.

Suppose you are to answer the following two questions: (1) Does the sentence "God exists" express a proposition? (2) If so, then is that proposition true or false? If you say no to the first question, then you may be classified as a noncognitivist with regard to God talk . If you say yes to it, thereby allowing that the given sentence does express a proposition, then you are a cognitivist with regard to God talk . (Let us henceforth abbreviate these expressions, simply using the terms "cognitivist" and "noncognitivist".) All theists, atheists, and agnostics are cognitivists, so the second question applies to them: is the proposition that God exists true or false? You are a theist if and only if you say that the proposition is true or probably true, you are an atheist if and only if you say that it is false or probably false, and you are an agnostic if and only if you understand what the proposition is, but resist giving either answer, and support your resistance by saying, "The evidence is insufficient" (or words to that effect).