Constituent and Component
Chapter Twenty-Six
Syllabus topic 2.1, "Distinctions between - proposition and sentence, proposition and judgment, proposition and fact, constituent and component."
Pages 126 to 129 of 334
In one line
A component of a proposition is a part that is itself a proposition; a constituent is a part that is not.
In the wording a student can write in an examination: the parts of a proposition are of two kinds. A component is a part which is itself a proposition, and which is therefore capable of being true or false on its own. A constituent is a part which is not a proposition, such as a term, and which is neither true nor false standing alone.
The distinction, shown
Take: "The notice was served."
Its parts are "the notice", "was served", and the copula. Not one of them is a proposition. "The notice" is not true and is not false; neither is "was served". So this proposition has constituents only.
Now take: "The notice was served and the rent was unpaid."
Its parts include "the notice was served" and "the rent was unpaid". Each of those is a proposition: each can be true or false on its own, and either may be true while the other is false. So this proposition has components. It also has constituents, because each component in turn has its own parts, but the presence of even one component is what matters.
The test
Take a part and ask: can it be true or false by itself?
If yes, it is a component. If no, it is a constituent.
Nothing more is required, and the test is worth stating in exactly those words because it also settles the harder cases.
"If the notice was served, the rent was payable." The parts "the notice was served" and "the rent was payable" can each be true or false on their own, so both are components, and the whole is a compound proposition. Note that neither is asserted here, as sequence 40 established. Being a component is not the same as being asserted.
"The notice served on 4 April was defective." Here "served on 4 April" looks like a proposition and is not one, because as it stands in this sentence it is a qualification of "the notice" and asserts nothing separately. It is part of the subject term, and therefore a constituent. This is the case students get wrong, and the test settles it: "served on 4 April", standing alone, is not true or false.
"Ravi believes the notice was served." The words "the notice was served" appear inside, and they can be true or false. But the whole is not made true or false by whether they are; it is made true by whether Ravi believes it. This is the one genuinely difficult case, and the standard treatment is that the embedded proposition is a component in form and that the whole is not truth-functional, which is why Module II's truth tables at sequence 350 do not reach propositions about belief.
Constituent and Component
Why the distinction matters
It is what "simple" and "compound" mean. A simple proposition has constituents only. A compound proposition has at least one component. That is the definition modern logic uses, and it is why MU sets this distinction at 2.1 and the kinds of simple and compound propositions at 2.6: the second cannot be stated without the first.
It tells you what can be symbolised as a unit. In the notation of sequence 350, a whole simple proposition is written with a single letter, p, because it has no propositional parts to expose. A compound proposition must be broken into its components before it can be symbolised at all.
It tells you what can be separately proved or disproved. A component can be admitted or denied on its own. A constituent cannot: denying "the notice" is not a possible move in a pleading, whereas denying "the notice was served" is.
A worked example
A section provides: "Where a tenant has been in arrears for three months and has failed to comply with a notice of demand, the landlord may apply for possession, unless the tenant deposits the arrears within thirty days."
Break it into components. Four parts can be true or false on their own:
p: the tenant has been in arrears for three months
q: the tenant has failed to comply with a notice of demand
r: the landlord may apply for possession
s: the tenant deposits the arrears within thirty days
Break one of them into constituents. In p, the parts are "the tenant", "in arrears" and "for three months". None is a proposition. They are constituents.
Why the exercise is worth doing. The section's structure is now visible: if p and q, then r, unless s. Four components, three connectives, and the whole is a compound proposition. Every dispute under the section will be about one of the four components, and the drafting question of what "unless" does to r is a question about a connective and not about any component.
And the trap. "A notice of demand" contains "demand", and "of demand" is not a proposition; it qualifies the notice. A reader who treated it as a component would produce a fifth item to prove that the section never required.
Distinctions that carry marks
| Constituent | Component | |
|---|---|---|
| Is itself a proposition | No | Yes |
| Can be true or false alone | No | Yes |
| Examples | the notice; was served; three months | the notice was served; the rent was unpaid |
| Found in | Every proposition | Compound propositions only |
| Can be separately denied | No | Yes |
Constituent and Component
| Simple proposition | Compound proposition | |
|---|---|---|
| Contains | Constituents only | At least one component |
| Symbolised as | A single letter | Components joined by connectives |
| Example | The notice was served. | The notice was served and the rent was unpaid. |
What this does not mean
A component need not be asserted. In a conditional, both components are present and neither is asserted. Presence and assertion are different questions.
A long constituent is still a constituent. "The notice served on 4 April at the registered office by a person authorised in that behalf" is one term however long, because it asserts nothing standing alone.
Component is not the same as clause. Grammar counts clauses; logic counts parts capable of truth and falsity, and the two lists differ, as the qualifying phrase in the worked example shows.
Quick revision
Component: a part of a proposition which is itself a proposition, and so can be true or false alone.
Constituent: a part which is not a proposition, such as a term.
The test: can this part be true or false by itself?
Simple proposition: constituents only. Compound proposition: at least one component. That is the whole basis of topic 2.6.
A component need not be asserted, as the parts of a conditional show.
Propositions about belief embed a component and are not truth-functional, which is why truth tables do not reach them.
Test yourself
1. Distinguish a constituent from a component and state the test.
A component of a proposition is a part which is itself a proposition, and which is therefore capable of being true or false on its own. A constituent is a part which is not a proposition, such as a term or a qualifying phrase, and is neither true nor false standing alone. The test is to take the part and ask whether it can be true or false by itself: if it can, it is a component, and if it cannot, it is a constituent.
2. Identify the components and constituents in "The notice was served and the rent was unpaid".
The components are "the notice was served" and "the rent was unpaid", each being a proposition capable of truth or falsity on its own, and either may be true while the other is false. The constituents are the parts of those components: "the notice", "was served", "the rent" and "was unpaid", none of which asserts anything standing alone.
3. How does the distinction define simple and compound propositions?
A simple proposition has constituents only and no components, so it cannot be broken into smaller propositions. A compound proposition has at least one component, and it is built out of propositions joined by connectives. The definition matters for symbolisation, since a simple proposition is written with a single letter while a compound one must be broken into its components before it can be written at all.
Constituent and Component
4. Is "served on 4 April" in "the notice served on 4 April was defective" a component?
No, it is a constituent. As it stands it qualifies "the notice" and forms part of the subject term; it asserts nothing separately and is neither true nor false standing alone. The whole proposition asserts one thing, that a particular notice was defective, and the reference to 4 April merely identifies which notice is meant.
5. Must a component be asserted?
No. In the conditional "if the notice was served, the rent was payable", both parts are components because each can be true or false alone, and neither is asserted: the proposition claims only that the second would follow from the first. Being a component is a question about whether the part is a proposition, not about whether the speaker has committed to it.
6. Why do truth tables not reach "Ravi believes the notice was served"?
Because the truth of the whole is not fixed by the truth of the embedded component. Whether the notice was served may be true or false without changing whether Ravi believes it, so the whole is not a truth function of its parts. Truth tables work only for compounds whose truth value is completely determined by the truth values of their components, which is the truth-functionality feature described at sequence 20.
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.