5. The Logic of Farabi is not a mere analysis of scientific thinking: it contains in addition many remarks on grammar, and discussions on the theory of knowledge. While grammar is limited to the language of one people, Logic, on the other hand, has to regulate the expression in language of the aggregate intelligence of mankind. From the simplest elements of speech it must advance to the most complex forms,—from the word to the sentence, and on to discourse. Logic falls into two divisions, according as its subjects stand related to actuality; the first of these comprising the doctrine of Ideas and Definitions (tasawwur), and the second, the doctrine of Judgments, Inferences, and Proofs (tasdiq). Ideas,—with which are classed Definitions, though in a mere loose, outward juxtaposition,—have in themselves no relation to actuality, that is to say, they are neither true nor false. Among ‘Ideas’ Farabi recognizes here the simplest psychological forms, that is, both the representations of individual objects arising from Sense-Perception, and those ideas which have been stamped upon the mind from the first, such as the Necessary, the Actual, the Possible. Such representations and ideas are immediately certain. A man’s mind may be directed to these, and his soul made observant of them, but they cannot be demonstrated to him, nor can they be explained by deriving them from what is known, seeing that they are already clear in themselves, and that too with the highest degree of certitude. By combining representations or ideas, judgments result, and these may be either true or false. To obtain a foundation for these judgments we have to go back through the processes of Inference and of Proof to certain propositions originally conveyed to the understanding, immediately obvious, and admitting of no farther confirmation. Such propositions,—the fundamental propositions or Axioms of all Science,—there must be for Mathematics, Metaphysics, and Ethics.