A talking animal or speaking animal is any non-human animal that can produce sounds or gestures resembling those of a human language. Several species or groups of animals have developed forms of communication which superficially resemble verbal language, however, these are not defined as language because they lack one or more of the defining characteristics, i.e. grammar, syntax, recursion and displacement. Researchers have been successful in teaching some animals to make gestures similar to sign language. However, these animals fail to reach one or more of the criteria accepted as defining language.
The term refers to animals which can imitate (though not necessarily understand) human speech. Parrots, for example, repeat things nonsensically through exposure. It is an anthropomorphism to call this human speech, as it has no semantic grounding.
Clever Hans was a horse that was claimed to have been able to perform arithmetic and other intellectual tasks. After formal investigation in 1907, psychologist Oskar Pfungst demonstrated that the horse was not actually performing these mental tasks, but was watching the reaction of his human observers. The horse was responding to involuntary cues in the body language of his trainer or other people who asked the horse questions and knew the answer but were unaware they were providing such cues.
A "formal language" requires a communication with a syntax as well as semantics. It is not sufficient for one to communicate information or even use symbols to communicate ideas.
Researchers have attempted to teach great apes (gorillas, chimpanzees, and bonobos) spoken language with poor results, and sign language with significantly better results. However, even the best communicating great ape has shown an inability to grasp the idea of syntax and grammar, instead communicating at best at the same level as a pidgin language in humans. They are expressive and communicative, but lack the formality that remains unique to human speech.