Is there a word or phrase that means to plant my idea in someone else’s mind so they think it is their own idea?
Just like what happened in the movie Inception.
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Consider the term insinuate. According to Collins English Dictionary it means
- (may take a clause as object) to suggest by indirect allusion, hints, innuendo, etc
- (transitive) to introduce subtly or deviously
- (transitive) to cause (someone, esp oneself) to be accepted by gradual approaches or manoeuvres
All three definitions suggest the type of seduction you allude to.
To inculcate may be used in the context described:
- To impress (something) upon the mind of another by frequent instruction or repetition; instill: inculcating sound principles.
- To teach (others) by frequent instruction or repetition; indoctrinate: inculcate the young with a sense of duty.
Source: The American Heritage® Dictionary of the English Language
You can "seed the idea" into someone's head, this is found in print e.g. in this novel. This would match your request that the people then think it their own idea, as who knows where the seed of a plant came from?
To expand on Scott's answer, the word suggest is the word you want for this. Its Latin roots are sub- ("from below") and -gerere ("to bring") and its literal definition is to evoke or bring to mind indirectly.
Prescriptively it has come into use as a term of direct entreatment ("I suggest we go to the store.") but its original roots are in subterfuge and insinuation ("What are you suggesting?")
This word gets to the heart of your request in all areas, as it covers the idea of stimulus (your "implanting") to one's thought (your "mind" requirement), but at a level that is undetected by the recipient (so they "think it is their own"). A psychological term, one definition of subliminal is:
existing or operating below the threshold of consciousness; being or employing stimuli insufficiently intense to produce a discrete sensation but often being or designed to be intense enough to influence the mental processes or the behavior of the individual (dictionary.reference.com)
Subliminal is an adjective that has no clear verb to relate it to, so as a "single-word-request" for a verb it does not work. Normally this adjective describes the effects of the particular type of communication used, so subliminal teaching, subliminal advertising, or subliminal message, etc. The closest single verb form I found was sublimate, which has a related, but slightly different idea behind it from a psychological perspective:
to divert the energy of (a sexual or other biological impulse) from its immediate goal to one of a more acceptable social, moral, or aesthetic nature or use. (dictionary.reference.com)
The idea of changing one's mind is there (to something "more acceptable" to the one doing the diverting), but it loses the subconscious idea. Combining the two, subliminally sublimate might work, but sounds very awkward. Better to stick with subliminal suggestion or other idea of expressing the communication (as noted above), or in your case perhaps subliminal implantation.
If you are writing such a work that you are able to define your own word, then you could add an ‑ate suffix and form a new word subliminate as a verb. However, you would need to find a way of describing what you mean by this new word within your text, so that people understand it is a verb formed from the idea of the adjective subliminal. Only your particular usage context could answer whether this option is open or not.
Inception is of course not the correct word as it means “the establishment or starting point of an institution or activity”, in this case the act or verb.
One could but should not in formal situations coin a term as to inceptionize, but that would just be for funzies.
On a side note, I did come across this from The Science of Creating Dreams:
Giving people dreams, however, is possible. We can create a form of dream and idea inception even without the cool devices used in the movie. In the movie, they paid homage to one method for successfully implanting ideas and dreams. When asked about giving people ideas, one of the characters noted that it is easy - just tell them to not think about something, like don't think about an elephant. Telling people to not think about something is what Daniel Wegner and his colleagues have been doing for years. In their classic work, they told people to not think about a white bear. Wegner has found that when people try to suppress a thought, they end up thinking about it more afterwards. Wegner refers to this as a rebound, or white bear, effect. The thought of a white bear rebounds after you try to suppress it.
Looking at the answers so far, I would say that the best phrase is already in your question, using the verb plant
Establish (an idea) in someone’s mind: