Online research in philosophy

In this paper we discuss the distinction between sentence and proposition from the perspective of identity. After criticizing Quine, we discuss how objects of logical languages are constructed, explaining what is Kleene’s congruence—used by Bourbaki with his square—and Paul Halmos’s view about the difference between formulas and objects of the factor structure, the corresponding boolean algebra, in case of classical logic. Finally we present Patrick Suppes’s congruence approach to the notion of proposition, according to which a whole hierarchy of congruences leads to different kinds of objects.

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?

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).

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.

“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..

Two quite different issues need to be addressed with regard to the sentence "God exists." One is whether or not the sentence expresses a proposition (something that is true or false and that can be believed or disbelieved). If we say, "Yes, it expresses a proposition," then the second issue comes in: Is that proposition true or false?[ 1].

The token in the box in this paper of a sentence does not express a proposition. Why not? Because if it did it would express a proposition that was, amongst other things, about this token of that sentence, and that thus said that it was not true. No proposition can say that of itself.

Barbara Partee is reported to have said that she never was sure whether the complement of an attitude verb should be a sentence or a proposition, where proposition is to be understood in a pre-theoretical sense as sentence meaning. In this paper we take up the question by investigation a suggestion made by David Kaplan in (Kaplan, 1977), viz. that the complement of an attitude is in fact a proposition, which is described by some character. Our answer to Partee's question is that the complement of a de re attitude is both a proposition and a sentence.

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.