science

Hurford disjunction

Hurford disjunction is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hurford disjunction rather than just read about it. In short: In formal semantics, a Hurford disjunction is a disjunction in which one of the disjuncts entails the other. The concept was first identified by British linguist James Hurford.

Key takeaways

Hurford disjunction belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hurford disjunction to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hurford disjunction from memory before moving on to harder problems.

Reference excerpt

In formal semantics, a Hurford disjunction is a disjunction in which one of the disjuncts entails the other. The concept was first identified by British linguist James Hurford. The sentence "Mary is in the Netherlands or she is in Amsterdam" is an example of a Hurford disjunction since one cannot be in Amsterdam without being in the Netherlands. Other examples are shown below:

#Tamina saw a Beatle or Paul McCartney. #The number I'm thinking of is divisible by 4 or it's even. #Is Wilbur a pig or an animal? As indicated by the octothorps in the above examples, Hurford disjunctions are typically infelicitous. Their infelicity has been argued to arise from them being redundant, since simply uttering the stronger of the two disjuncts would have had the same semantic effect. Thus, they have been taken as motivation for a principle such as the following:

Local Redundancy: An utterance is infelicitous if its logical form contains an instance of a binary operator ⊕ {\displaystyle \oplus } applied to arguments A {\displaystyle A} or B {\displaystyle B} , whose semantic contribution is contextually equivalent to that of either A {\displaystyle A} or B {\displaystyle B} on its own. However, some particular instances of Hurford disjunctions are felicitous.

Sofia ate some of the pizza or all of it. Henrietta is five feet tall or six feet tall. Felicitous Hurford disjunctions have been analyzed by positing that the weaker disjunct is strengthened by an embedded scalar implicature which eliminates the entailment between the disjuncts. For instance, in the first of the felicitous examples above, the left disjunct's unenriched meaning is simply that Sofia ate a nonzero amount of pizza. This would result in a redundancy violation since eating all the pizza entails eating a nonzero amount of it. However, if an embedded scalar implicature enriches this disjunct so that it denotes the proposition that that Sofia ate some but not all of the pizza, this entailment no longer goes through. Eating all of the pizza does not entail eating some but not all of it. Thus, Local Redundancy will still be satisfied.

Worked examples

Example 1 — a first encounter with Hurford disjunction

Start with the simplest possible case. Write down what Hurford disjunction claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hurford disjunction before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hurford disjunction ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hurford disjunction

In research: Hurford disjunction appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hurford disjunction in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hurford disjunction is common in secondary-school and first-year university syllabi. It links to neighbouring topics Formal semantics (natural language), Linguistics stubs, Logic, so understanding it makes those chapters shorter.
In everyday life: Look for Hurford disjunction outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Hurford disjunction in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hurford disjunction means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hurford disjunction out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hurford disjunction in simple terms?

In formal semantics, a Hurford disjunction is a disjunction in which one of the disjuncts entails the other. The concept was first identified by British linguist James Hurford.

Why does Hurford disjunction matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hurford disjunction?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hurford disjunction.