new
5
new
6 wholesome
7 8 not-new Notice that the common description wholesome appearsin the centre. So, if we number the sections of the boardnot-new as shown, then new corresponds to the upper regions, 1,2,5 and 6; nice corresponds to the left-hand regions 1,3,5 and 7; and wholesome corresponds to the central regions, 5,6,7 and 8. For example, region 6 contains the new not-nice unwholesome 3 the not-new 4 (“Remarkable untempting cakes!�, wholesome cakes, and region 4 containes not-nice unwholesome cakes as Carroll observed).
Numbering the board
Transferring
The object is to eliminate the centre and obtain a bilateral diagram representing the conclusion. To do this, we look at the propositions one at time, starting with any negative ones. In general, we consider negative statements first, since they are enable us to place grey counters with certainity. The second proposition, No nice cakes are unwholesome
nice
not-nice
1 new
2 5
n
6 wholesome
7
not-new 3
8
not-ne
unwholesome
4
Dealing with the nice cakes
This tells us that none of the cakes in the left half (the nice cakes) lies in the centre (the wholesome cakes). This means that region 1 and 3 are empty, and we indicate this by placing grey counters in these regions: Next we consider the first proposition, 1 Some new cakes are unwholesome
nice
not-nice 2
This tells us that some of the cakes in the top half (the new cakes) do not lie in the centre. We can indicate this by new 5 6 a grey counter There are no cakes here), so placing a red counter in region 1 or region 2. But region 1 already contains we must place our red counter in region 2:
wholesome
not-new
7
210
unwholesome
8