I've had students like Loughner as he was when Slinker knew him; they are actually not all that uncommon at community colleges. The comment about handing in pages of geometrical symbols rather than what was actually assigned is very familiar. Such students are generally bright and creative, but either lack discipline of mind, have a sense of relevance that is very weak, or have very undeveloped capacity for self-critique. To say that they have scrambled brains is not really fair; rather, they have scrambled backgrounds of one sort or another that have resulted in a need to learn systematically what most people pick up as they go along -- a need which ordinary class situations aren't usually suited to fulfill. Temperamentally, some of them are troubled, some of them are very sweet; in either case, however, I don't think that what is usually taught in introductory philosophy classes is healthy for them. I'm very pleased that Slinker tried to work with Loughner to find alternative assignments; that's exactly what such students usually need. It's very sad that Loughner didn't respond to the offers.
I have to say something about this, though:
The odd thing about Loughner's syllogisms is that they're not far off from examples Slinker might use in class. "When you teach logic, you draw a distinction between truth and inference," says Slinker. To illustrate that, a teacher might say, "If chickens could fly upside down, then George W. Bush would be president in 2098." The statement isn't true. It just serves as a premise from which to draw conclusion.
Conditional statements of almost any sort are logical bugbears: they're everywhere and they are almost everywhere hard to pin down logically. How to interpret indicative conditional statements is a matter of some controversy; there's a standard way to do it, as a material conditional (i.e., as meaning the same as 'either the antecedent is false or the consequent is true'), but the primary reason that this is the standard way to interpret such statements is just that it's the easiest, being a relatively simple interpretation that can be used with relatively simple logical rules. When teaching propositional logic one typically gets around this by making stipulations left and right to guarantee that conditional statements act like material conditionals, but natural language is not always so hospitable. But what we are dealing with in the above conditional is a subjunctive or counterfactual conditional statement, and subjunctive conditionals in natural language make indicative conditionals look like easy little puzzles. Consider the following two subjunctive conditional statements:
If John were in Tokyo, he'd be in Australia.
If John were in Tokyo, he'd be in Japan.
Suppose that John is neither in Australia nor Japan. Thus if we were to misread these as indicative conditionals, all the antecedents and consequents are false. But while the first conditional statement is false, the second is true. There are about a jillion different accounts of why this might be so, all with troubles of one sort or another. But because subjunctive conditional statements are stubbornly resistant to easy logical analysis, when faced with a conditional statement like, "If chickens could fly upside down, then George W. Bush would be president in 2098," we can't say whether the conditional is false unless we know the context in sufficient detail to be able to say what the relationship between chickens flying upside down and Bush being president in 2098 is.
This is why one tries to stick to indicative statements in basic logic; I would shy away from an example like the above if I could at all avoid it, and if I had to use it for some reason, I'd feel compelled to add all the qualifications that drive my students up the wall. I doubt that Slinker actually uses examples like this very much in class; if he's like anyone else, he uses indicative conditionals. It's notable in this regard that Loughner's syllogisms are all basic modus ponens and modus tollens syllogisms, using only indicative conditionals. This is why they often sound stilted and repetitive; the awkwardness of the English is not due to grammatical incompetence but due to the fact that he is pushing and pulling the language so that it fits the logical form. But it's not odd that Loughner's syllogisms look like teaching examples for basic logic in a philosophy class: that's clearly where he picked up the habit. And I don't think it's difficult to see why he took to it. Logic has a paradoxical character some students have difficulty with and some students revel in: it's both very structured and very free, like dreams or Alice in Wonderland.