Question 3·Hard·Words in Context
In her landmark 1975 paper Randomness and Recursive Functions, mathematician Julia Robinson demonstrated that the apparent randomness of certain number sequences was in fact the product of strict logical constraints, thereby ______ the common intuition that unpredictability and order are mutually exclusive.
Which choice completes the text with the most logical and precise word or phrase?
For SAT words-in-context questions, first paraphrase the sentence in your own words, paying special attention to contrast words (like "but," "however") and cause-effect phrases (like "thereby"). Decide whether the blank needs a word that shows agreement, disagreement, cause, result, or something else. Then, before looking too closely at the choices, state the general idea the blank should express (for example, "challenging a belief" or "adding support"). Finally, eliminate choices whose core meanings (confirming, complicating, illustrating, etc.) don’t match that idea or clash with the tone, and pick the one whose basic meaning and direction fit the sentence best—even if its exact definition is unfamiliar, use roots, prefixes, and the overall sentence logic to guide you.
Hints
Use the demonstration to understand the effect on the intuition
Ask yourself: if something that seems random is actually produced by strict logical constraints, does that make the common intuition about unpredictability and order look correct or incorrect?
Determine the overall direction: support or challenge?
Is the author presenting Robinson’s work as evidence that the usual way people think about unpredictability and order is right, or as evidence that this usual way of thinking needs to be rejected?
Group the answer choices by their general "direction"
Which options suggest supporting a belief, which suggest challenging it, and which are more neutral? Cross out any choices that would keep the common intuition intact.
Step-by-step Explanation
Understand what Robinson demonstrated
Focus on the descriptive clause: she "demonstrated that the apparent randomness of certain number sequences was in fact the product of strict logical constraints." This means that sequences that look random are actually governed by clear, strict rules—there is order beneath the apparent unpredictability.
Connect that idea to the "common intuition"
The "common intuition" mentioned is that "unpredictability and order are mutually exclusive"—that if something is unpredictable, it cannot be ordered, and vice versa. But Robinson shows that what looks unpredictable is actually produced by strict logical (ordered) constraints, which directly contradicts that intuition, rather than supporting it.
Decide what kind of verb is needed in the blank
Because her work shows the intuition is not correct, the blank must be filled with a verb that describes challenging or undermining that intuition, not one that confirms it, merely complicates it, or uses it as an example.
Match each option’s meaning to the sentence and choose the best fit
Now consider the choices:
- reaffirming = confirming again or strengthening a belief (the opposite of what the sentence describes)
- complicating = making something more complex or harder to understand (doesn’t capture that the intuition is wrong)
- confuting = proving something to be false or invalid
- exemplifying = serving as an example of something Since Robinson’s result shows the common intuition is wrong, the only verb that fits is C) confuting.