 If “particulars” means what it usually means in such a context, namely existentially quantified statements, then this is just wrong: existentially quantified statements are hardly ever major premises in syllogisms. But as Mallet points out, the passage makes sense if the “universal premises” are statements like (**) and their “particulars” are corresponding statements of the form  (*).  Al-Fārābī is then saying that natural language syllogisms are validated through being instances of universal rules stating that all arguments of a certain form are valid. If this is a correct reading, it makes al-Fārābī a formal logician in a strong sense. And indeed some writers have written about al-Fārābī’s “formalism” (Zimmermann 1981: xl).