Question

Kelly broke a lamp and was told that she had been bad. later that evening, she was told that her parents were getting a divorce. she thought that her breaking the lamp had caused the divorce. this is an example of what kind of reasoning?

Answer 1

This is a classic example of transductive reasoning.

This term originated from and was first used by Jean Piaget who used it in his description of children in their per-operational stage of development. This kind of reasoning focuses on concrete incidents and events or instances and does not follow neither deductive nor inductive reasoning. 
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Answer 2

This is an example of transductive reasoning, this type of reasoning is normal in children aged 2-4 years. This error of reasoning occurs when children mistakenly assume that if one situation follows another, the first is responsible for the second. In this example, Kelly broke the lamp and then her parents divorced, so she deduced that breaking the lamp caused a divorce.