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

The Aims of Logic

By Arthur N. Prior on NA/NA/1950

This text has been transcribed by David Jakobsen, Aalborg University, [removed] and Martin Prior

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I.

The Aims of Logic
1

A.N. Prior


The traditional aim of logic is to sort out good forms of argument from bad ones. But this aim
needs a little explanation.


An argument or inference takes us from a certain premiss, or from certain premisses, to a certain

conclusion. We may write the premiss or premises first and then write the conclusions provided by
“therefore” or “so” or “hence”, thus:
-
2

Nothing evil is created by God;

Everything real is created by God;

Therefore (or

so, or hence) nothing real is evil.


Or we may write the conclusion first and then w
rite the premisses preceded by
“for” or “since” or
“because”, thus:
-

Nothing real is evil, for (or since, or because)

n
ot
hing evil is created by God, +
3

everything real is created by God.


The premisses, wher
ever placed, are the statements or propositions
from
which the
conclusion is
drawn or inferred;

the conclusion is the statement or {page 2} proposition inferred from the
premiss. In common speech the conclusion is often said to be a deduction or inference
from the
premis
s
es, but logicians prefer to use the term “deduction” or “inference” for the entire argument


premiss or premisses, conclusion and the word (“so”, “for” or whatever it might be) which shows
which is which.


Different inferences may be of th
e same “form”. For example, the inferen
ce given above is of the
same f
o
r
m as the following:
-

Nothing combustible is safe to use;

Everything in

this
house is
safe to use;

Therefore nothing in this house is combustible.
4


The form of an inference is commonly exhibited by replacing those words which do not contribute
to it by schematic letters. Thus both of the above inferences have the form

Nothing (that is) Y is Z;




1

Edited by Martin Prior and David Jakobsen.
Editors’ note: At the top of the page is written
, not by Prior


Was this the
beginning of that VI
th

for
m Logic Book A
*

was asked to write?


Martin is not sure whether the last

part of the sentence
is written by Mary but the first part of it
looks as if it could be
.

*’A’ is written on top of ‘he’
. This is perhaps written in
1950, though a mention of tenses in part II could suggest that Prior wrote this after his invention of ten
se
-
logic.

2

Editors’ note: The following has been struck through: No Christians are Communists; Therefore (or so) no
Communists are Christians.

3

Editor’s note: Prior uses ‘+’ for ‘and’ in his notes and letters.

4

Editor’s no
te: In 1946 and in 1949 the hom
e of Mary and Arthur burned down.

The use of this example is a slight
indication that it could have been written in 1950. The flat in Cashmere Hills burned down in March 1949 and for some
9 month, Martin Prior recollects, they had been renting.

Everything (that is) X is Z

Therefore nothing (that is) X
is Y.




The statements or propositions which occur as premisses or conclusions in inferences

may be
true or false. An inference as a whole, however, is not true or false, but valid (or sound) or invalid
(or unsound). An inference is valid if and only if no inference of that form takes us from a true
premiss, or from premisses {page 3} all of whic
h are true, to a false conclusion. A particular
inference may not itself do this, but if other inferences of the same form do so, the inference is still
invalid (unsound, unsafe)


its premisses do not really warrant (imply, entail) its conclusion. For
exa
mple, the inference


Every three
-
sided figure is three
-
angled

Therefore every three
-
angled figure is three
-
sided,


d
oes not itself take us from a true premiss to a false conclusion, but from a true to a true; but it is
invalid all the same, for

other infe
rences of the same f
o
r
m, e.g.

Every blind man is disabled
,

Therefore every disabled man is blind,


do take us from a true premiss to a false conclusion. We may say that the from


Every XY is Z


Therefore every XZ is Y


is

an invalid form of inference. Particular inference
s

of this form may not lead us astray, but others
would.


Note that an inference is not rendered invalid mere
ly by having a false conclusion;

for if we
arrive by inference at a false conclusion the blame f
or this may be not with the form of inference
used but with the false premisses from which we start. We are not then “led astray” {page 4} by the
inference,
but were “astray” to begin with;

and indeed we may come to see that some assumption
we have made is

false precisely by seeing that a false conclusion may be validly drawn from it. For
example, the following inference is valid:
-


No mammal lays eggs;


The platypus is a mammal;


Therefor
e

the pla
t
ypus does not lay egg
s
.


But its conclusion is false;

so one of its premisses must be (in fact the first one is).


So a valid inference with a false conclusion must have at least one false premiss. But a valid
inference with a false premiss need not have a false conclusion. For example, the following valid
i
nference has two false premis
s
es but its conclusion is true:
-

{page 5}


All birds are motor
-
cars;


All motor
-
cars have feathers;


Therefore all birds have feathers.


# To sum up:

A valid inference may take us from truth to truth, or from falsehood to falsehood, or from falsehood
to truth; but never from truth to falsehood


an inference taking us from truth to falsehood is not
valid but invalid. And even if a particular inference d
oes not take us from truth to falsehood, it is
invalid if other inferences of exactly the same form
5

{page 6} do so. So the aim of logic is to find
forms of inference which will never take us from truth to falsehood
.
6




5

Editors’
note: The following passage has been struck out: It is necessary to say “of
exactly

the same form” since a
form of inference which is not itself valid may have special cases


sub
-
forms


which
are
valid. For example, “No A is
a B, therefore no B is a C” i
s an invalid form of inference (“No horse is a dog, therefore no dog is an animal”, which is
of this form, takes us from a truth to a falsehood), but the special sub
-
variety of this form in which C is the same as A is
perfectly valid. (“No horse is a dog,
therefore no dog is a horse” is valid; it exemplifies the …

6

Editors’ note: The following passage has been struck out:


What looks like a different way of stating the aim of logic, or at all events the aims of logic, is to say that it attempts
to
defeat
inconsistencies.

In fact this is a by
-
product of the aim already stated. Two propositions are inconsistent if they
cannot both be true, and they are formally inconsistent if, in any pair of propositions of the same form …


If one proposition may be
validly inferred from another, we sometimes say that it is
deducible from
that other, or
that the other
entails

it. So …

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