science

No–no paradox

No–no paradox 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 No–no paradox rather than just read about it. In short: The no–no paradox is a distinctive paradox belonging to the family of the semantic paradoxes (like the Liar paradox). It derives its name from the fact that it consists of two sentences each simply denying what the other says.

Key takeaways

No–no paradox belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect No–no paradox to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of No–no paradox from memory before moving on to harder problems.

Reference excerpt

The no–no paradox is a distinctive paradox belonging to the family of the semantic paradoxes (like the Liar paradox). It derives its name from the fact that it consists of two sentences each simply denying what the other says.

History A variation on the paradox occurs already in Thomas Bradwardine’s Insolubilia. The paradox itself appears as the eighth sophism of chapter 8 of John Buridan’s Sophismata. Although the paradox went largely unnoticed even during 20th-century revival of semantic paradoxes, it has recently been rediscovered (and dubbed with its current name) by the American philosopher Roy Sorensen, and is now appreciated for the distinctive difficulties it presents.

Formulation The notion of truth seems to be governed by the naive schema:

(T): The sentence ' P ' is true if and only if P (where we use single quotes to refer to the linguistic expression inside the quotes). Consider however the two sentences:

(N1): (N2) is not true (N2): (N1) is not true Reasoning in classical logic, there are four possibilities concerning (N1) and (N2):

Both (N1) and (N2) are true Both (N1) and (N2) are not true (N1) is true and (N2) is not true (N1) is not true and (N2) is true Yet, possibilities 1. and 2. are ruled out by the instances of (T) for (N1) and (N2). To wit, possibility 1. is ruled out because, if (N1) is true, then, by (T), (N2) is not true; possibility 2. is ruled out because, if (N1) is not true, then, by (T), (N2) is true. It would then seem that either of possibilities 3. and 4. should obtain. Yet, both of those possibilities would also seem repugnant, as, on each of them, two perfectly symmetrical sentences would mysteriously diverge in truth value.

Discussion Generally speaking, the paradox instantiates the problem of determining the status of ungrounded sentences that are not inconsistent. More in particular, the paradox presents the challenge of expanding one’s favourite theory of truth with further principles which either express the symmetry intuition against possibilities 3. and 4. or make them acceptable in spite of their intuitive repugnancy. Because (N1) and (N2) do not lead to inconsistency, a certain strand in the discussion of the paradox has been willing to assume both the relevant instances of (T) and classical logic, thereby deriving the conclusion that either possibility 3. or possibility 4. holds. Such conclusion has in turn been taken to have momentous consequences for certain influential philosophical theses. Consider, for example, the thesis of truthmaker maximalism:

(TM): If a sentence is true, there is something that makes it true If, as per possibilities 3. and 4., one of (N1) or (N2) is true and the other one is not true, then, given the symmetry between the two sentences, it might seem that there is nothing that makes true whichever of the two is in fact true. If so, (TM) would fail. These and similar conclusions have however been contested by other philosophers on the grounds that, as evidenced by Curry's paradox, joint reliance on (T) and classical logic might be problematic even when it does not lead to inconsistency.

References

Worked examples

Example 1 — a first encounter with No–no paradox

Start with the simplest possible case. Write down what No–no paradox 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 No–no paradox 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 No–no paradox 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 No–no paradox

In research: No–no paradox 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 No–no paradox 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: No–no paradox is common in secondary-school and first-year university syllabi. It links to neighbouring topics Concepts in logic, Grammar, Meaning (philosophy), so understanding it makes those chapters shorter.
In everyday life: Look for No–no paradox 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 No–no paradox in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what No–no paradox 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 No–no paradox out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is No–no paradox in simple terms?

Why does No–no paradox 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 No–no paradox?

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 No–no paradox.