STATEMENTS

What is a statement? As mentioned in chapter 1, this apparently innocent question can lead us quickly into deep philosophical waters. A statement cannot be just a sentence, since sentences have a great variety of linguistic functions.

We use them not only to make statements, but to ask questions, issue commands, make exclamations, exhortations, and so forth. But these other functions are by and large identifiable by their grammatical moods, interrogative (“Are you going?”), and Imperative (“Go!,” “Let’s go!”). So why not say a statement is a sentence (in indicative or perhaps subjunctive mood) used to make an assertion, i.e., a declarative sentence! This is close. But the same statement is made by the following three different declarative sentences: “It is raining,” “П pleut,” and “Es regnet,” the second and third being French and German for the first. And if I say “It is raining” twice in a row, have I made two statements or one? Is “Sean Penn was divorced by Madonna” a different statement than “Madonna divorced Sean Penn”?

These difficulties can be resolved as follows. First we need to distinguish a type of sentence from a token of the same sentence. Thus a declarative sentence such as “It is raining” is one that could be uttered or written on many different occasions by different people. Each such utterance or act of writing is a token of that sentence-type. Second, among types of sentence we may distinguish the declarative sentence (which, when written down or spoken, is subject to grammatical rules), from the proposition (what is expressed by a declarative sentence, its content or meaning). Thus “It is raining” is one sentence, and tokens of it may be uttered on any number of occasions. “П pleut” and “Es regnet” are different sentences, but express the same proposition. Likewise “Sean Penn was divorced by Madonna” and “Madonna divorced Sean Penn”: statements in the passive mode (“S was divorced by M”) express the same proposition as corresponding active mode statements (“M divorced S”), and from here on will always be so reinterpreted.

Now clearly statements in the sense of utterances are no concern of logic; nor are sentences insofar as they are mere grammatical items.

Consequently logic has been said to deal with statements in the last of these senses only, types of statements that are propositions: hence the traditional name for the logic of statements, “Propositional Logic.” In the twentieth century, however, the notion of propositions came in for trenchant criticism on the grounds that no one has been able to give an adequate account of when two propositions couldbe regarded as identical. As a result, most logic texts define a statement as “a sentence that is either true or false.” Butthere are difficulties with this definition too, as noted above and discussed further in the Glossary under statement; see also proposition.

Fortunately, we need not resolve this philosophical issue in order to proceed. The definitions already given in chapter 1 of statement and proposition are adequate for our purposes:

A statement is a sentence (or part of a sentence) that expresses something true or false.

But to say a statement is true or false is just to say what it asserts is true or false. Thus in this sense, i.e., semantically, a statement maybe Identifiedwithwhat it expresses, namely the proposition, which we defined as follows:

A proposition is what a statement expresses as true or false.^[10]

In contrast to this, a question may ask whether something is true or false, but it does not express something that is true or false. Similarly, a command such as “Do up your shoe laces!” does not assert anything true or false; nor does an exhortation such as “Let’s go, Blue Jays!” Finally a supposition such as “Suppose you are right” does not itself assert the statement “you are right,” although the latter statement is contained within the supposition.

3.1.2

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Source: Arthur R.T.W.. An Introduction to Logic: Using Natural Deduction, Real Arguments, a Little History, and Some Humour. Broadview Press,2016. — 456 p.. 2016

STATEMENTS

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