PKOCEBDINGS 
OF THE 
LITERA.EY AND PHILOSOPHICAL SOCIETY. 
Ordinary Meeting, October 7th, 1879. 
J. P, Joule, D.C.L., LL.D., F.RS., &c.. President, in the 
Chair. 
“ On an extension of the Ordinary Logic, connecting it 
with the Logic of Relatives,” by Joseph John Mukphy, 
F.G.S. Communicated by the Rev. Robekt Haeley, M.A., 
F.RS. 
All logic deals with relation, and in this paper the common 
logic is treated as being that branch of the logic of relatives 
which deals with the relations of inclusion and exclusion. 
The proposition of the common logic “All A is B ” is here 
expressed by “ A is included in B,” or “ A is an enclosure of 
B.” The converse of this, as commonly stated, is “ Some B 
is A ; ” but this is insufficient, because when reconverted it 
only gives back “ Some A is B,” and reconversion ought to 
give back the original proposition. The converse form here 
proposed is “ B includes A,” or “ B is an includent of A.” 
When all M is A and all M is B, the conclusion is ex- 
pressed in the common logic by “Some A is B.” This 
syllogism is here expressed thus : — “ A is an includent of M ; 
B is an includent of M ; therefore A and B are co-includents 
of M ; ” or if we drop the M, “ A and B are co-includents.” 
When all A is M and all B is M, there is no conclusion 
recognised by the old logic ; yet there is a valid conclusion, 
which here appears in the following syllogism : — “ A is an 
Peoceedings — Lit. & Phil. Soc. — Yol. XIX. — Xo. 1 . — Session 1879-80. 
