Evincing Kamp's own example (personal communication), if we analyze the sentences One of the three candidates is over forty and Two of the three candidates are under forty by traditional means, we are unable to account for the important difference between them, namely that the former can, while the latter cannot, be followed by We eliminate him. This vantage point lets us see DRT, and semantic theory in general, as an explicit reconstruction of structural, inferential patterns governing our use of language carried out via explicating the roles of individual expressions within these patterns.
We are not given all the multiplications in the enumerative sense, but we are given all in one sense: any multiplication can be carried out according to rule.
It is a simple matter to make up a statement which will agree with experience because it is such that no proposition can refute it, e.g., "There is a white rabbit between two chairs whenever no observations or verifications are being carried out.
The difference between a reason and a cause is brought out as follows: the investigation of a reason entails as an essential part one's agreement with it, whereas the investigation of a cause is carried out experimentally.
Scientific inference may really sometimes be abductive; but then, science is social, whereas quotidian cognition, of the kind psychologists care about, is carried out in single heads.
But as the matter is often carried farther, even to the absolute rejecting of all profound reasonings, or what is commonly called metaphysics, we shall now proceed to consider what can reasonably be pleaded in their behalf.
It is probable, that one operation and principle of the mind depends on another; which, again, may be resolved into one more general and universal: and how far these researches may possibly be carried, it will be difficult for us, before, or even after, a careful trial, exactly to determine. This is certain, that attempts of this kind are every day made even by those who philosophize the most negligently: and nothing can be more requisite than to enter upon the enterprize with thorough care and attention; that, if it lie within the compass of human understanding, it may at last be happily achieved; if not, it may, however, be rejected with some confidence and security.
And though they have sometimes carried the matter too far, by their passion for some one general principle; it must, however, be confessed, that they are excusable in expecting to find some general principles, into which all the vices and virtues were justly to be resolved.
Every passion is mortified by it, except the love of truth; and that passion never is, nor can be, carried to too high a degree.
Or in other words; having found, in many instances, that any two kinds of objectsâflame and heat, snow and coldâhave always been conjoined together; if flame or snow be presented anew to the senses, the mind is carried by custom to expect heat or cold, and to believe that such a quality does exist, and will discover itself upon a nearer approach.