Let us see what we can make of the two Premisses--


"All Dragons are uncanny;
All Scotchmen are canny."


Remember, I don't guarantee the Premisses to be FACTS. In the
first place, I never even saw a Dragon: and, in the second place,
it isn't of the slightest consequence to us, as LOGICIANS, whether
our Premisses are true or false: all WE have to do is to make out
whether they LEAD LOGICALLY TO THE CONCLUSION, so that, if THEY
were true, IT would be true also.

You see, we must give up the "Cakes" now, or our cupboard will
be of no use to us. We must take, as our 'Universe', some class
of things which will include Dragons and Scotchmen: shall we say
'Animals'? And, as "canny" is evidently the Attribute belonging
to the 'Middle Terms', we will let m stand for "canny", x for
"Dragons", and y for "Scotchmen". So that our two Premisses are,
in full,


"All Dragon-Animals are uncanny (Animals);
All Scotchman-Animals are canny (Animals)."


And these may be expressed, using letters for words, thus:--