. The London, Edinburgh and Dublin philosophical magazine and journal of science. and (2) Fromwhat combination of arguments may we conclude that A andH are both true when E and Gr are both false ? Representing truth by a capital and falsity by a small letter,all possible combinations of the truth or falsity of the eightarguments are indicated by the small squares in the followingdiagram. The shaded squares indicate the A combinations which areinconsistent with one or more of the premises; the non-Acombinations, not being required in the conclusion, may beneglected. The first part of the conclu
. The London, Edinburgh and Dublin philosophical magazine and journal of science. and (2) Fromwhat combination of arguments may we conclude that A andH are both true when E and Gr are both false ? Representing truth by a capital and falsity by a small letter,all possible combinations of the truth or falsity of the eightarguments are indicated by the small squares in the followingdiagram. The shaded squares indicate the A combinations which areinconsistent with one or more of the premises; the non-Acombinations, not being required in the conclusion, may beneglected. The first part of the conclusion calls for the eightcombinations numbered 1 to 8 on the diagram. These are :— AB cDEFGH AB cDEFGA AB cd E ¥ g H AB cd E¥ g h Ab cDE F g H Ab cDe FGH Ab. cBe F Gth Ab cd e Fg H and one or other of these is true. It will be observed that inall the combinations C is false and F true. Many subordinate Diagrams for n Terms. 269 conclusions may be drawn, such as A, B, and D being alltrue, E, F, and G are also true; A being true when B and Gare both false, H is true, & m iHHHi mwm III1-1 ^ 1—H M ? hi in The second part of the conclusion calls for the three combi-nations marked 8 to 10 on the diagram. These areA b c d e¥ gB. A b c D ef gR. Hence from either B C D/ or b c D e or b c d e we may con-clude AegH. Attention may be drawn to the fact that these diagramsdiffer from those suggested by Mr. Venn in having a compart-ment for the absence of all the characters or objects. Thus inthe 8-term diagram the compartment marked with a starstands for the combination abedefgh. This compartmentmay need to be shaded out, and hence should be indicated ona complete logical diagram. This is parenthetically acknow- 270 Mr. E. H. M. Bosanquet on the History of the ledged by Mr. Venn ( Symbolic Logic, p. 271), and practi-cally in the construction of bis logical-diagram machine(Symbolic Logic/ p. 122); I have constructed a logical-diagram machine on the basisof these diagrams. Blocks, cor
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