The problem of other minds is a consequence of mind–body dualism, specifically the idea that there is no necessary relation between physical bodies and their behavior, on the one hand, and mental processes, on the other. Descartes’ famous “I think therefore I am” expresses a basis for certainty concerning the existence of our own mental life. But on what basis can we infer that other people have minds? Descartes invoked the benevolence of God as a reason to trust our inferences regarding other minds. Why would God have given us such a clear and distinct apprehension of other minds if they did not exist ?
Non-theological attempts to justify our belief that other people have minds have generally rested on a kind of analogy, also discussed by Descartes and emphasized by Locke  and other British empiricists such as J.S. Mill . The analogy uses the known relation between physical and mental events in oneself to infer the mental events that accompany the observable physical events for someone else. For example, as shown in Fig. 1, when I stub my toe, this causes me to feel pain, which in turn causes me to say “ouch!” When I see Joe stub his toe and say “ouch,” I infer by analogy that he feels pain.
The problem with this analogy is that it begs the question. Why should I assume that same behavioral–mental relations that hold in my case also hold in Joe’s? Joe could be acting and not really feel pain. He could even be a robot without thoughts or sensations at all. The assumption that analogous behavior–mental state relations hold for other people is essentially what the analogy is supposed to help us infer.
(1) Descartes doesn't hold that we have a clear and distinct apprehension of other minds. He holds instead (in the Discourse) that we infer that people have minds from their flexible use of language and their rational behavior. He doesn't tell us in the Discourse what the status of this inference is; but (e.g.) Arnauld in his book on true and false ideas is easily able to adapt them into God-is-not-a-deceiver arguments, and that is reasonably plausible given other things Descartes says. But if we had a clear and distinct apprehension of other minds, we wouldn't need such arguments.
(2) Whatever problems the argument from analogy may have, question-begging is not one. "Why should I assume that same behavioral–mental relations that hold in my case also hold in Joe’s?" But, of course, you aren't assuming it; you are concluding it on the basis that they do hold in your case. The reasoning is causal (as Farah recognizes):
this kind of behavior : this kind of cause :: that extremely similar kind of behavior : X
Given that similars are similar, it is not unreasonable to conclude that X is an extremely similar kind of cause, particularly where there is no evidence of another cause of such behavior. That the inference is non-monotonic -- which is all the acting and thoughtless robot cases show -- is not to the point.
It's also worth pointing out that the analogical argument for other minds is not based on single bits of evidence (like Joe's saying 'ouch'), but on vast amounts of evidence (all our experience of ourselves and other people), and this same vast pool of evidence allows you to make the analogy much more sophisticated than can be done if you are considering only one brief instance. (Whether there is any plausibility to the claim that Joe is acting or that he's really a thoughtless robot, i.e., whether these are live possibilities, is determined from the same pool of evidence. For that matter, so is the plausibility of the claim that the brain has something to do with mental function, which plays such a key role in Farah's argument later in the paper.)
But the paper is worth reading, and makes some interesting arguments.