On the Correct Usage of 'Infers' and 'Implies'

Within the space of a few days, I caught two TV pundits and an otherwise competent writer misusing 'infer.' Why do people have such a  difficult time with the distinction between inference and implication?  I will try to explain the matter as simply as I can.

The test to determine whether a use of 'infer' is correct is whether or not the thing said to be inferring is a mind. If it is a mind, then the use is correct; if it is not a mind, then the use is incorrect.  Some examples:

• The author's citations infer that Serling drew inspiration from a diverse group of authors and philosophers. This use of 'infer' is incorrect because a citation is not a mind, and so cannot engage in any such mental operation as inference. 'Imply' would be correct.
• Seeing Tom's car in front of Sally's house, Bill inferred that Tom was visiting Sally. Correct. It is correct because the thing doing the inferring, Bill, is an entity capable of the mental operation of drawing a conclusion from one or more premises.
• Pelosi's 'astroturf' remark inferred that protesters at town hall meetings are organized agitators. Incorrect. A remark is the content of a remarking; it is something that a person says. What a person says is not a mind but a proposition, and a proposition, not being a mind, cannot infer anything. 'Implied' would be correct.
• Pelosi implied that town hall protesters are organized agitators when she made her 'astroturf' comment. This is a correct use of 'implied.' But note that 'imply' has two main uses. One is the strictly logical use according to which implication is a relation between propositions. The other is the nonlogical use according to which implication is a relation between a person (or a mind) and a proposition. Pelosi implied that the protesters are organized in the sense that she suggested that this is so. In most cases one can substitute 'suggests' for 'implies' when the latter is employed nonlogically.
• Are you implying that I'm a liar? This is a correct use of 'implying.' The word is being used in the nonlogical sense just explained. One can replace the question salva significatione with 'Are you suggesting that I'm a liar?'
• Are you inferring that I am a liar? This is also correct inasmuch as the addressee may indeed be inferring that the speaker is a liar. The addressee may be concluding from the speaker's shifty eyes and other 'body language' that he is not telling the truth.
• What you said infers that I'm a liar. This is incorrect because what a person said cannot engage in any mental operations such as the operation of drawing a conclusion from a premise. 'Implies' would be correct. 'Implies' would then be being used to express a relation between two propositions.

In sum, inference is the mental operation of drawing a conclusion from one or more premises.  Only minds can infer.  So uses of 'infer' and cognates are correct only  in application to minds.  Any use of 'infer' that implies that a nonmind can engage in inference is incorrect.  So the following is incorrect: Any use of 'infer' that infers that a nonmind can engage in inference is incorrect.    Implication in its strictly logical sense in a relation between propositions.  Hence the slogan: Only minds infer; only propositions imply.

Unfortunately for the slogan, the water is muddied by the fact that 'implies' has the two distinct uses lately explained.  So here is a more accurate slogan: Only minds infer; only propositions logically imply, though persons can conversationally imply.