To make an inference is to form a new belief on the basis of an old one. Here is an example. My friend Larry has been evicted from his apartment. I let him stay with me until he finds a new place to live. I notice that, shortly after Larry moves in, all of my money and valuables start disappearing. I also notice that purchases that I didn’t make are appearing on my credit card bills. I know that nobody other than Larry had access to my money, valuables, and credit cards. So I infer that Larry has stolen my money and valuables and illicitly used my credit cards.
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