ABSTRACT
IT seems to be sufficiently proved in the preceding Lecture, that Reasons truly and properly speaking do of themselves admit no Quantity, no Reason, nor therefore can one be predicated greater, lesser, or equal with Respect: to another, because of any Thing inherent in, or agreeing with themselves; but these Attributes are derived from the absolute Quantums upon their Reasons, But because Custom has so long prevailed to have Reasons compared together like absolute Quantums, and the Names of an Equal, a Greater, or a Lesser Reason has obtained, and we do not unwillingly admit these Expressions with due Caution; it next follows that we enquire by what certain Sign or Mark it may be known, when a Reason may be said to be equal to another, when greater, when lesser, i. e. how a Reason can be defined and distingushed greater, lesser, or equal. And indeed it seems plainly enough to follow from what has been said, that, if two Reasons consisting of homogeneous Terms have a common Consequent, they may be most appositely defined by the respective Quantities of their Antecedents, viz. so that those are to be called Equal Reasons whose Antecedents are Equal, this greater than that, when the Antecedent of this is greater than the Antecedent of that, and this lesser than that, when the Antecedent of this is lesser than the Antecedent of that. But since it often falls out that Reasons of a different Consequent are compared, and Consequently this Condition fails, therefore some other universal Sign is required to discover the Relation of those Reasons, which may be sufficient for determining the Habitudes of all Reasons to one another. And we have hitherto found it a Thing of great Difficulty to find such a sufficient Sign; since various Causes hinder, especially two, viz. the Difference between Effable and Ineffable Reasons (i. e. the Incommen-surability of Quantities) and the Heterogeneity of the Terms of which different Reasons consist. For if all Reasons were Effable, and only between commensurable Quantities, an Equal Reason might be the same Way defined with the Proportionality of Numbers in the fifth Element, viz. by the equal Quotients of the Divisions, and a Greater and a Lesser Reason by the Inequality of the Quotients respectively: but the Incommensurability of the Terms of most Reasons hinders this from being universal, by which it happens that the Division cannot be performed exactly, nor expressed in common Numbers, nor the Manner whereby the Terms respect one another clearly conceived. Also the Heterogeneity of the Terms of the Reasons compared exclude some other Ways deviseable, whereby the Reasons of the Reasons might be otherwise defined, which perhaps shall be hereafter shewn. Hence it seems very difficult to exhibit any Universal Mark, by which it may plainly and certainly be pronounced concerning the Equality or Inequality of any two Reasons proposed, whose Terms are indifferently commensurable or incommensurable, homogeneous or heterogeneous.
