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Whether ontological matters must be demonstrated.
Since science is the habit habit original: habitus; in this context, it refers to a mental disposition or a stable skill acquired through practice of demonstrating assertions (§ 30 Preliminary Discourse); those things proposed in Ontology must be demonstrated.
Indeed, the treatment by the Scholastics Scholastics original: Scholasticorum; the medieval university philosophers. Wolff critiques them for using complex words without clearly defining them or proving their points logically was sterile because they did not attend to the form of the demonstrative method. Instead, they were content with confused, and even occasionally entirely obscure notions, and remained distant from specific propositions and their internal reasons.
Objection and response.
But if you deny that Ontology is rightly defined as a science, and from this infer that it is wrongly concluded that things proposed within it must be demonstrated: I shall show by the opposite reasoning that the demonstrative method must be used in Ontology, and from this conclude that it is a science.
To be sure, nominal definitions nominal definitions original: definitiones nominales; definitions that explain the meaning of a word rather than the essential nature of the thing itself are arbitrary, and it is quite sufficient—once you have established their reality—that you can use them as principles of demonstration (§ 790 Logic). However, we show through the work itself that Ontology can be treated with the demonstrative method; thus, there is no need to prove the reality of the definition by any other means (§ 719 Logic). Nevertheless, lest those not yet sufficiently skilled in Logic original: Logicæ should hesitate when they come to examine our work, we shall also enter upon a second path for their sake.
Special reasons why the demonstrative method suits ontology.
The demonstrative method must be used in first philosophy. If, in Logic, Practical Philosophy, and Physics, as well as Natural Theology, General Cosmology, and Psychology, everything must be rigorously demonstrated; then ontological principles must very often be used (§ 89, 92, 94, 96 and following, Preliminary Discourse). Consequently, nothing should be admitted in Ontology unless it is sufficiently explained and rests upon both indubitable experience and demonstration (§ 562 Logic). Therefore, the demonstrative or scientific method must be used within it (§ 790 and following, Logic).
I suppose, of course, that in the aforementioned disciplines, certain knowledge must be handed down. It is well established, however, that when the philosophical method is neglected (§ 137 Preliminary Discourse)—and consequently the scientific method (§ 792 Logic)—certain knowledge cannot be obtained without indubitable experience and demonstration (§ 567, 570 Logic).