I think the analysis of the hypo forgets to start by analyzing if there was a breach of a duty. Looking to proximate cause first can be like putting the cart before the horse, and can just leave you ending up confused.
The closest analogy to that hypothetical is Palsgraf, where the (possible) tort to one person could not form the basis for a finding of a breach of duty to third person. So, a restaurant serving Patron A bad food is not a breach of its duty to Patron Z (unless A and Z are married (or parent and child, etc.) and Z sues to get loss of consortium). However, the possible exception would be if it was foreseeable that the tort to the one person would harm others. You could argue that the restaurant should have foreseen that the sick patron would throw up and cause the premises to become unsafe. (Of course, it would have to be a tortious act, and serving bad food is not always a tort).
The hypo could end up with the restaurant liable for the slip-and-fall damages, though, even without finding that it was foreseeable that the person would create a dangerous condition by throwing up. People/businesses owe a duty to invitees (which the patron would be), and part of that duty is to keep the premises safe. If the restaurant had actual or constructive notice of the dangerous condition on the floor (the vomit), then there would be a breach of that duty, and that breach could easily be the proximate cause of the injuries.
That sound right?
"The above is the most correct response. There are 2 types of causation u need to prove. Factual (but-for) and Proximate (substantial factor test). Also, look at superceding causes - whether a specific defendant's action relieves another defendant from liability (I think it's easier to use a foreseeability test in place of substantial factor). For example, if you eat at a restaurant and get sick and throw up and patron slips on your vomit can patron sue the restaurant for serving you bad food? Serving bad food is a factual cause (but-for) but probably not proximate cause (substantial factor) in patron slipping and falling (we learned foreseeable harm/victim test which might be easier to apply). The superceding cause is you vomiting all over the floor. Restaurant serving bad food seems a bit removed from patron's slipping and falling... not a substantial factor to injury suffered."