(3) Put the Proposed Premisses into subscript form.
(4) Select two which, containing between them a pair of codivisional Classes, can be used as the Premisses of a Syllogism.
(6) Find a third Premiss which, along with this Conclusion, can be used as the Premisses of a second Syllogism.
(8) Proceed thus, until all the proposed Premisses have been used.
(9) Put the last Conclusion, which is the Complete Conclusion of the Sorites, into concrete form.
[As an example of this process, let us take, as the proposed Set of Premisses,
(1) "All the policemen on this beat sup with our cook; (2) No man with long hair can fail to be a poet; (3) Amos Judd has never been in prison; (4) Our cook's 'cousins' all love cold mutton; (5) None but policemen on this beat are poets; (6) None but her 'cousins' ever sup with our cook; (7) Men with short hair have all been in prison."
Univ. "men"; a = Amos Judd; b = cousins of our cook; c = having been in prison; d = long-haired; e = loving cold mutton; h = poets; k = policemen on this beat; l = supping with our cook pg089 We now have to put the proposed Premisses into _subscript_ form. Let us begin by putting them into _abstract_ form. The result is
(1) "All k are l; (2) No d are h'; (3) All a are c'; (4) All b are e; (5) No k' are h; (6) No b' are l; (7) All d' are c."
And it is now easy to put them into _subscript_ form, as follows:--
(1) k_{ 1}l'_{ 0} (2) dh'_{ 0} (3) a_{ 1}c_{ 0} (4) b_{ 1}e'_{ 0} (5) k'h_{ 0} (6) b'l_{ 0} (7) d'_{ 1}c'_{ 0}
We now have to find a pair of Premisses which will yield a Conclusion. Let us begin with No. (1), and look down the list, till we come to one which we can take along with it, so as to form Premisses belonging to Fig. I. We find that No. (5) will do, since we can take k as our Eliminand. So our first syllogism is
(1) k_{ 1}l'_{ 0} (5) k'h_{ 0} .'. l'h_{ 0} ... (8)
We must now begin again with l'h_{ 0} and find a Premiss to go along with it. We find that No. (2) will do, h being our Eliminand. So our next Syllogism is
(8) l'h_{ 0} (2) dh'_{ 0} .'. l'd_{ 0} ... (9)
We have now used up Nos. (1), (5), and (2), and must search among the others for a partner for l'd_{ 0}. We find that No. (6) will do. So we write
(9) l'd_{ 0} (6) b'l_{ 0} .'. db'_{ 0} ... (10)