The Nachlass of A.N. Prior
a joint project between
Department of Information Studies - University of Copenhagen
Department of Communication and Psychology - Aalborg University

The Seven Logical Relations

By Arthur N. Prior on NA/NA/1966

This text has been transcribed by Martin Prior and Peter Øhrstrøm

Download the PDF of this item
Please note that this text is extracted from the PDF, and is as such most likely not styled properly.
The Seven Logical Relations

A.N. Prior

Some years ago (in 19 …) Susan Stebbing

produced a little popular introduction to logic called
Logic in Practice
, in which one of the main topics

was the “seven logical relations” in which one
proposition may stand to another. She called them …

Now a popular introduction, called
Elementary Formal Logic
, has been produced by C.L. Hamblin

of the University of New South Wales, this being a “programmed c
ourse of the ‘linear’ type
which sample questions
and answers following short explanations, point by point. (I can imagine
this book being useful in a variety of ways e.g. as an adjunct to
an adult education course, or as a
means for breaking down the initial hopelessness of many beginners in University logic courses; it
is in any case a nice bit of field work by one of the main living experts on the logic of question and
answer). And in {2}

this book a prominent place is given to the “seven logical relations”. And

so; they do make an excellent “lead in”

for the people for whom Hamblin is writing, and for
whom Stebbing wrote before. But now that they
being thus brought before us a
gain, it may be a
good time to say a little about them, from both a historical and systematic point of view.

Hamblin speaks, in this connex
ion, of “this ancient piece of doctrine”, and refers to them as the

sical” logical relations, in a


in which the contrast is clearly with “modern”
(rather than, say, with “intuitional”). I suppose a book
which can still be so like Stebb
ing in 1966
could be said to have an antique air, but in fact Hamblin’s doesn’t, and this is anyhow not what he
The seven relations were not of course Stebbing’s invention. But so far as I can find out they
were not counted or listed as seven until 1906.

Their history appears to be as follows:

W.S. Jevons, in his
Principles of Science

(1874), Chapter 6,
observed th
at anyone “Any one proposition or gr
oup of propositions may be class
ed ….”


The partial text is kept in the Prior collection at Bodleian Library, Oxford. It has been edited by Martin Prior and Peter
Øhrstrøm. It has not been dated, but since Hamblin's book was published in 1966, it was probably written shortly after.


Susan Steb
Logic in Practice
, Methuen & Co. Ltd., 1934.


Prior does not list the seven relations in this MS, but it is usually claimed that propositions may be (1) equivalent, (2)
related as principal to subaltern, (3) related as subaltern to principal, (4) in
dependent, (5) subcontraries, (6) contraries or
(7) contradictories, cf. Morris Raphael Cohen, Ernest Nagel, John Corcoran,
An Introduction to Logic
, Hackett
Publishing, 1993, p. 56.


C.L. Hamblin,
Elementary Formal Logic: A Programmed Course
1966. •  University of Copenhagen •  Aalborg University •