Quaternlo terminorum 135
John is the father of Peter, and the father of Peter is the father of Paul, so
John is the father of Paul.
(There are three terms, and this is valid.)Quaternio terminorum can result is endless confusion in daily
relationships. If John is in debt to Peter to the tune of 45 dollars,
and Peter is in debt to Paul (who saved him from drowning),
John might be very surprised to find Paul on his doorstep
demanding money with menaces. On the other hand, if John is
in love with Mary, and Mary is in love with Paul, no one except a
theatre dramatist would attempt to complete the fallacious
deduction.
The four-terms fallacy is more likely to appear as a source of
genuine error than of deliberate deception. People may fool
themselves with arguments constructed around it, but they are
unlikely to fool others. There is something about the odd look of
it which alerts the unwary; it is like a cheque without the amount
filled in. No date perhaps; maybe even no signature; but
everyone looks at the amount.
China is peaceful towards France, and France is peaceful towards the
USA, so China must be peaceful towards the USA.
(You do not even need to know anything about China to know this is
wrong. Just remember not to trust any relationship with France in it.)One way to use the fallacy with a fair chance of success is to
smuggle it in amongst a group of comparatives. Comparatives,
such as 'bigger than', 'better than', 'stronger than', or 'fatter
than', do work because they are transitive, despite the four
terms. After a few of these, slip in the non-transitive relationship
and it might get by.