Aristotle's lost work On Ideas is reported by Alexander of Aphrodisias to have summarized four main arguments for Plato's theory of Ideas: (1) the Argument from Sciences (79.3-80.6), which states that if every science refers to one, rather than many, objects of thought then for each science there must be one everlasting Idea; (2) the Argument from One Over Many (80.8-81.22), which states that if many subjects truly share the same predicate, which is self-predicated, but distinct from every subject, then this predicate must be one Idea that perfectly exemplifies the predicate; (3) the Argument from Thought (81.25-82.7), which states that whenever we think of anything, we must think of some enduring being, rather than perishable beings, so that anything thought must endure as an Idea beyond perishable beings; and (4) the Argument from Relatives (82.11-83.33), which states that whenever one predicate is predicated of many subjects, the predication is true either (a) equivalently [identically], (b) metaphorically [differently], or (c) paradigmatically [identity-in-difference]. (cf. Fine 1993) These four arguments produce a single conception in which the Ideas are the (1) first principle of science, (2) one concrete universal subsuming many particulars, (3) enduring rather than perishing, and (4) absolutely self-related simple entities. Aristotle’s objects that (i) the arguments (1-4) only result in common predicative concepts rather than separately subsisting Ideas, and (ii) the truth of the arguments admit some Ideas that must either be denied by the Platonist or are somehow contrary to the theory of Ideas (e.g. crafts, non-being, or unequals). While the (ii) latter objection can be answered by further specifying the theory of Ideas, the (i) former objection might suggest an alternative Aristotelian theory, in which the Ideas are merely formal essences localized in particular substances.