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What is the term of the state in which one acts to be very experienced even though he does not appear to know everything. And, because of his confidence, is able to persuade people that he/she is right?

The person may think that his/her knowledge is enough, but actually the world is much bigger than his experience.

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I think you are referring to the Dunning-Kruger Effect. It describes the relationship between experience one has in a particular topic and his/her confidence about being an expert.

Dunning and Kruger argue that when people know nothing, they also know that they know nothing. However, after learning only a little bit, people seem to be very confident that they understand everything of the subject.

enter image description here

With more studying, one realizes that there is more to it and might feel insecure even. However, after studying more and more and more and people become an expert, people begin to realize that they do know a lot, but that it is impossible to understand everything.

Both the x- and y-axis have no scales because the Dunning-Kruger effect is only conceptual. The following image, does nicely present the train of thoughts through the graph:

enter image description here

References

Kruger, J., & Dunning, D. (1999). Unskilled and unaware of it: how difficulties in recognizing one's own incompetence lead to inflated self-assessments. Journal of personality and social psychology, 77(6), 1121.

Pictures taken from: https://www.linkedin.com/pulse/dunning-kruger-effect-confidence-vs-over-confidence-harshil-rastogi

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    $\begingroup$ This is exactly what I was searching for. Thank you, please do whatever my question for others to be beneficial $\endgroup$ – mmonem May 3 '17 at 10:02
  • $\begingroup$ I wonder if the trough is related to Impostor Syndrome? Can one's confidence level be far below what it should be relative to actual state of knowledge? $\endgroup$ – user9634 Jun 2 '17 at 20:45
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Another theory/study by Leonid Rozenblit and Frank Keil, is the illusion of explanatory depth.

This powerful but inaccurate feeling of knowing is what Leonid Rozenblit and Frank Keil in 2002 termed, the illusion of explanatory depth (IOED), stating, “Most people feel they understand the world with far greater detail, coherence, and depth than they really do.”

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