·-----------------------------------------------------· | | ·-------· | | ·-------· | | | | (.) | | | |( )|( )| | | Some x exist | |---|---| | No x exist | |---|---| | | | | | | | | | | | | | | ·-------· | | ·-------· | |---------------|-----------|-------------|-----------| | | ·-------· | | ·-------· | | | | | | | | | | | | | Some x' exist | |---|---| | No x' exist | |---|---| | | | | (.) | | | |( )|( )| | | | ·-------· | | ·-------· | |---------------|-----------|-------------|-----------| | | ·-------· | | ·-------· | | | | | | | | |( )| | | | Some y exist | |(.)|---| | No y exist | |---|---| | | | | | | | | |( )| | | | | ·-------· | | ·-------· | |---------------|-----------|-------------|-----------| | | ·-------· | | ·-------· | | | | | | | | | |( )| | | Some y' exist | |---|(.)| | No y' exist | |---|---| | | | | | | | | | |( )| | | | ·-------· | | ·-------· | ·-----------------------------------------------------· Similarly we may represent the seven similar Propositions "All x are y'", "All x' are y", "All x' are y'", "All y are x", "All y are x'", "All y' are x", and "All y' are x'". Let us take, lastly, the Double Proposition "Some x are y and some are y'", each part of which we already know how to represent. ·-------· |(.)|(.)| |---|---| | | | ·-------· Similarly we may represent the three similar Propositions, "Some x' are y and some are y'", "Some y are x and some are x'", "Some y' are x and some are x'". The Reader should now get his genial friend to question him, severely, on these two Tables. The _Inquisitor_ should have the Tables before him: but the _Victim_ should have nothing but a blank Diagram, and the Counters with which he is to represent the various Propositions named by his friend, e.g. "Some y exist", "No y' are x", "All x are y", &c. &c. pg035 TABLE III.