ABSTRACT
I consider a language w ith quantifiers 3 and V, as defined in Chapter 1 . 1 2 . As I did in Chapter 1 , I begin by considering general deductive situations M = > v , and I ask again for fair and reasonable hypotheses about a deduc tion in order to conclude that there also is a deduction leading to a formula 3 x w or to a formula V x w . Let w (t) denote a substitution instance arising from w by substituting the term t for x in w ; then in the first case an ob vious answer is
(13) If M ==> w (t) is a deduction for the particular case of some t , then it should be possible to conclude that there is a deduction M = > 3 x w .
In the same manner, I ask for fair and reasonable hypotheses about a deduction in order to conclude that there also is a deduction leading to a formula u from a formula 3 x w , or from a formula V x w , together w ith further assum ptions M . This tim e, in the second case an obvious answer is
