ratiocinate
verb

- to make judgments about something based on sensible thinking or logic

The Cambridge Dictionary

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WORD ORIGIN

“Ratiocinate" derives from the Latin verb ratiocinari, meaning "to compute, calculate, or reason,” and is formed from ratio (meaning "reason, calculation, or account") and the verb-forming suffix -cinari.

The root ratio in Latin originally referred to computation or calculation before extending to mean reasoning or thinking logically. It shares its origin with other English words like "rational," "ratio," and "reason."

"Ratiocinate" entered English in the mid-17th century (around the 1650s) during a period when many scholarly terms were being borrowed from Latin. It was primarily used in philosophical and logical contexts to describe the process of reasoning or drawing logical conclusions through a step-by-step thought process.

While "ratiocinate" is not so common in everyday English usage, it continues to appear in philosophical, logical, and literary contexts. Its specialized meaning of "to reason methodically and logically" has remained remarkably stable over the centuries, unlike many words that undergo significant semantic shifts.

The related noun "ratiocination" refers to the process of exact thinking or a reasoned train of thought, particularly emphasizing formal or logical reasoning.

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THE DESERT ISLAND PUZZLE
Can you avoid getting bogged down with the following puzzle?

A blind man is alone on a deserted island. He has 2 blue pills and 2 red pills. He must take exactly one red pill and one blue pill or he will die.

If he takes two of these pills at random there is no guarantee that he’ll get exactly one red and one blue pill.

Question: How does he ensure his survival?

Scroll down for a hint.

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Hint: Think about the possibility of breaking the pills into pieces.

Or scroll down for the solution.

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THE SOLUTION

First take any pill and cut it into 2 halves, retain one half and throw the other half away.

Then take the next pill, cut it into 2 halves, retain one half and throw the other half away.

Repeat the same procedure for the remaining 2 more pills.

Following that process what is left behind are 4 halves: 2 half-red pills and 2 half-blue pills,… equaling one full-red and one full-blue pill.

Puzzle solved! :-)

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SYNONYMS

analyze, apply logic, appraise, assess, balance the pros and cons, break it down, calculate, cerebrate, check the facts, chew on (over), cogitate, come to a reasoned conclusion, compute, connect the dots, critically evaluate, deduce, draw conclusions, engage in logical thinking, evaluate, exercise one's grey cells, figure (out), follow a chain of reasoning (the logic, the thread), get to the bottom of, infer, join the dots,  lay it out, line up the facts, make connections (deductions, sense of), map out, mull (over), piece together, ponder, put on one's thinking cap, put two and two together, puzzle out, rack one's brains, RATIOCINATE, rationalize, reason (logically, out, through), reflect, ruminate, run the numbers, see the big picture (the forest for the trees), speculate, stew, structure one's thoughts, synthesize, take a logical approach, theorize, think (critically, deeply, it through, logically, methodically, rationally, step by step, straight, systematically, things over, things through), turn over in one's mind, unravel, use deductive reasoning (inductive reasoning, logical reasoning, one's brain, one's common sense, one's head, one's mind, one's noodle), weigh evidence (options), work out

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SMUGGLE OWAD into an English conversation, say something like:

“Here’s a puzzle involving a blind man on a desert island,… but you’ll need to RATIOCINATE in order to solve it.”

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