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A counterintuitive proposition is one that does not seem likely to be true when assessed using intuition or gut feelings.

Scientifically discovered, objective truths are often called counter-intuitive when intuition, emotions, and other cognitive processes outside of deductive rationality interpret them to be wrong. However, the subjective nature of intuition limits the objectivity of what to call counter-intuitive because what is counter-intuitive for one may be intuitive for another.

Flawed understanding of a problem may lead to counter-productive behavior with undesirable outcomes. In some such cases, counter-intuitive policies may then produce a more desirable outcome. For example, a policy of catching large fish and throwing back small ones so may be counter-productive. In response to that policy, evolutionary pressure may select for small fish. A counter-intuitive improvement may be to catch only medium sized fish, leaving the biggest free to breed, creating evolutionary pressure for fish to grow quickly through the medium size.^[1]

Many scientific ideas that are generally accepted by people today were formerly considered to be contrary to intuition and common sense.

For example, most everyday experience suggests that the Earth is flat; actually, this view turns out to be a remarkably good approximation to the true state of affairs, which is that the Earth is a very big spheroid. Furthermore, prior to the Copernican revolution, heliocentrism, the belief that the Earth goes around the Sun, rather than vice versa, was considered to be contrary to common sense.

Another counter-intuitive scientific idea concerns space travel: it was initially believed that highly streamlined shapes would be best for re-entering the earth's atmosphere. In fact, experiments showed that blunt-shaped re-entry bodies make the most efficient heat shields when returning to earth from space. Blunt-shaped re-entry vehicles have been used for all manned-spaceflights, including the Mercury, Gemini, Apollo and Space Shuttle missions.

The Michelson-Morley experiment sought to measure the velocity of the Earth through the aether as it revolved around the Sun. The result was that it has no ether velocity at all. Relativity theory later explained the results, replacing the conventional notions of ether and separate space, time, mass, and energy with a counter-intuitive four-dimensional non-Euclidean universe.

• Common sense
• Folk physics
• Folk psychology
• Paradox
• List of paradoxes

The following topics are commonly considered to be counterintuitive:

• Wave-particle duality / photoelectric effect - is light a wave or a particle?
• Proof that 0.999... equals 1 - some people find this difficult to accept
• Squaring the circle - intuition suggests it's possible; it isn't
• The violation of the monotonicity criterion in voting systems
• The Monty Hall problem poses a simple yes-or-no question from probability that even professionals can find difficult to reconcile with their intuition.

1. ^ New Scientist, July 2005