What a Proposition Is
Chapter Twenty-Four
Syllabus topic 2.1, "Distinctions between - proposition and sentence, proposition and judgment, proposition and fact, constituent and component."
Pages 117 to 120 of 334
In one line
A proposition is what a sentence says when the sentence is capable of being true or false.
In the wording a student can write in an examination: a proposition is the meaning expressed by a declarative sentence, and it is the unit that bears truth and falsity. The sentence is the form of words; the proposition is what those words assert.
Why the distinction is the first thing in Module II
Because the whole module is about classifying propositions, and it cannot be done on sentences. Sentences differ from one another in ways that make no logical difference at all, and treating them as the unit produces a classification of grammar rather than of thought.
Three facts make the point, and every one of them is asked.
One proposition, many sentences. "Ravi paid the money", "The money was paid by Ravi" and "It was Ravi who paid the money" are three sentences, differing in voice and in emphasis. They assert the same thing, and any one of them is true exactly when the others are. There is one proposition here and three sentences.
One proposition, many languages. A sentence in English and its correct translation into Marathi are two sentences and one proposition. If propositions were sentences, translation would be impossible in principle, and the fact that a witness may be examined through an interpreter would be inexplicable.
One sentence, many propositions. "I was there yesterday" expresses a different proposition every time a different person says it, and a different one again on a different day. The sentence is the same. What it asserts is not.
Which sentences express propositions
Grammar recognises four kinds of sentence and only one of them expresses a proposition.
Declarative sentences assert something and express propositions: "The notice was served."
Interrogative sentences ask: "Was the notice served?" Nothing is asserted, so nothing is true or false.
Imperative sentences command or request: "Serve the notice." Again nothing is asserted.
Exclamatory sentences express feeling: "How careless!"
Only the first can be a premise or a conclusion, which is the rule already used at sequence 30. This is not a grammatical nicety; it is why a plaint contains statements and a prayer clause, and why only the statements can be traversed in a written statement.
Two cautions. A sentence in the interrogative form may nevertheless assert something: a rhetorical question is an assertion wearing a question mark, and it is treated as the proposition it asserts. And a sentence in the declarative form may assert nothing determinate, as vague and ambiguous sentences do, which is the subject of the reduction chapter at sequence 300.
Proposition and statement
Some books use "statement" where this book uses "proposition", and MU's own reading list contains both usages. Nothing turns on it for this paper. Where a distinction is drawn, "statement" is the act of stating and "proposition" is what is stated, which parallels the distinction between judgment and proposition in the next chapter.
What a Proposition Is
The safe course in an examination is to say that a proposition is what is capable of truth or falsity, and to note that some writers call it a statement. That is accurate and costs one line.
A worked example
A written statement contains the following sentence: "It is denied that the defendant received any notice, and in any event, was the notice not sent to an address the plaintiff knew to be wrong?"
How many propositions? Two, and the second is disguised.
The first is asserted by the opening clause: that the defendant received no notice.
The second is put in interrogative form, but it is a rhetorical question and it asserts that the notice was sent to an address the plaintiff knew to be wrong. Reduced to a proposition, it is capable of truth or falsity, and it can be traversed, put to a witness and found upon.
Why the distinction matters here practically. A pleading is a set of propositions, and every one of them must be capable of being admitted or denied. Anything in a pleading that is not a proposition, an exclamation, a question, an expression of indignation, is unanswerable and therefore has no place there. Rewriting a rhetorical question as the proposition it asserts is not pedantry: it is what allows the other side to plead to it.
Distinctions that carry marks
| Sentence | Proposition | |
|---|---|---|
| What it is | A form of words | What the words assert |
| Belongs to | A language | No language in particular |
| True or false | Not itself | Yes; it is the bearer of truth |
| Relation | Many sentences may express one | One proposition, many sentences |
| Changes with | Voice, word order, language | Nothing except what is asserted |
| Kind of sentence | Example | Expresses a proposition |
|---|---|---|
| Declarative | The notice was served. | Yes |
| Interrogative | Was the notice served? | No, unless rhetorical |
| Imperative | Serve the notice. | No |
| Exclamatory | How careless! | No |
What this does not mean
A proposition is not a sentence written carefully. It is not a form of words at all. Two entirely different forms of words express one proposition when they assert the same thing.
A proposition is not a fact. That distinction is the next chapter's, and it is the one most often confused.
Not every declarative sentence expresses a determinate proposition. "He came fairly soon after that" is declarative and, without more, asserts nothing definite enough to be true or false. Making such sentences definite is the work of sequence 300.
What a Proposition Is
Quick revision
Proposition: what a declarative sentence asserts; the bearer of truth and falsity.
Sentence: a form of words in a particular language.
One proposition, many sentences: active and passive, different word orders, different languages.
One sentence, many propositions: "I was there yesterday", said by different people on different days.
Only declarative sentences express propositions. Interrogative, imperative and exclamatory sentences do not, though a rhetorical question asserts what it appears to ask.
"Statement" is used by some writers for the same thing; where distinguished, the statement is the act and the proposition is what is stated.
Test yourself
1. Distinguish a proposition from a sentence.
A sentence is a form of words belonging to a particular language; a proposition is what a declarative sentence asserts, and it is the thing that is true or false. The two are distinct because one proposition can be expressed by many sentences, in different voices, different word orders and different languages, while one sentence can express different propositions on different occasions of its use.
2. Give an example of one proposition expressed by three sentences.
"Ravi paid the money", "The money was paid by Ravi" and "It was Ravi who paid the money". The three differ in voice and emphasis and are identical in what they assert: each is true in exactly the circumstances in which the others are true. Since truth and falsity attach to the proposition and not to the wording, there is one proposition here and three sentences.
3. Give an example of one sentence expressing different propositions.
"I was there yesterday." Spoken by the plaintiff on 5 April it asserts that the plaintiff was at the place on 4 April; spoken by the defendant on 9 April it asserts something entirely different, about a different person and a different day. The words are the same throughout, so what varies must be the proposition and not the sentence.
4. Which kinds of sentence express propositions, and why does it matter in a pleading?
Only declarative sentences, since only they assert something capable of truth or falsity. It matters in a pleading because a pleading is a set of propositions each of which must be capable of being admitted or denied. A question, a command or an exclamation cannot be traversed, cannot be put to a witness and cannot be found upon, so anything in a pleading that is not a proposition has no work to do there.
5. What is a rhetorical question, and how is it treated?
A sentence in interrogative form that in fact asserts something, being asked for effect rather than for an answer. It is treated as the proposition it asserts, since what matters logically is what is being claimed and not the punctuation. In a pleading or an argument it should be rewritten as the assertion it is, so that it can be answered.
What a Proposition Is
6. Why can Module II not classify sentences instead of propositions?
Because sentences differ in ways that make no logical difference, such as voice, word order, emphasis and language, so a classification of sentences would be a classification of grammar. The classifications in this module, into categorical and conditional, into A, E, I and O, and into simple and compound, all turn on what is asserted, which is the proposition. Two sentences asserting the same thing must fall in the same class, and they do only if the proposition is the unit.
The rest of this subject
These notes are cut from the University's printed syllabus. Open the syllabus itself, or the past papers, for the same subject.