As the process is simply the reverse of that discussed in the previous Chapter, we can avail ourselves of the results there obtained, as far as they go. First, let us suppose that we find a _Red_ Counter placed in the North-West Cell. ·-------· |(.)| | |---|---| | | | ·-------· We know that this represents each of the Trio of equivalent Propositions "Some xy exist" = "Some x are y" = "Some y are x". Similarly we may interpret a _Red_ Counter, when placed in the North-East, or South-West, or South-East Cell. Next, let us suppose that we find a _Grey_ Counter placed in the North-West Cell. ·-------· |( )| | |---|---| | | | ·-------· We know that this represents each of the Trio of equivalent Propositions "No xy exist" = "No x are y" = "No y are x". Similarly we may interpret a _Grey_ Counter, when placed in the North-East, or South-West, or South-East Cell. pg037 Next, let us suppose that we find a _Red_ Counter placed on the partition which divides the North Half. ·-------· | (.) | |---|---| | | | ·-------· We know that this represents the Proposition "Some x exist." Similarly we may interpret a _Red_ Counter, when placed on the partition which divides the South, or West, or East Half. * * * * * Next, let us suppose that we find _two Red_ Counters placed in the North Half, one in each Cell. ·-------· |(.)|(.)| |---|---| | | | ·-------· We know that this represents the _Double_ Proposition "Some x are y and some are y'". Similarly we may interpret _two Red_ Counters, when placed in the South, or West, or East Half. * * * * * Next, let us suppose that we find _two Grey_ Counters placed in the North Half, one in each Cell. ·-------· |( )|( )| |---|---| | | | ·-------· We know that this represents the Proposition "No x exist". Similarly we may interpret _two Grey_ Counters, when placed in the South, or West, or East Half. * * * * * Lastly, let us suppose that we find a _Red_ and a _Grey_ Counter placed in the North Half, the _Red_ in the North-_West_ Cell, and the _Grey_ in the North-_East_ Cell. ·-------· |(.)|( )| |---|---| | | | ·-------· We know that this represents the Proposition, "All x are y". [Note that the _Half_, occupied by the two Counters, settles what is to be the _Subject_ of the Proposition, and that the _Cell_, occupied by the _Red_ Counter, settles what is to be its _Predicate_.] pg038 Similarly we may interpret a _Red_ and a _Grey_ counter, when placed in any one of the seven similar positions