G.E. MOORE
GAVE A DIFFERENT
DEFINITION OF “ INTERNAL RELATION ”
AND DIAGNOSED AN ERROR OF THE
ABSOLUTE IDEALISTS
.
G. E. MOORE 1873-1958

WE GIVE A (SLIGHTLY)
SIMPLER EXPLANATION OF
MOORE’S POINT
CONSIDER THE FOLLOWING STATEMENT:
(1) “ NECESSARILY, IF A HAS PROPERTY P , THEN
IF X DOES NOT, THEN X IS NOT IDENTICAL
WITH A .”
HERE WE ARE SUPPOSING THAT P IS A
RELATIONAL PROPERTY, BUT IT DOESN’T
REALLY MATTER.

IF A THING A HAS ANY PROPERTY THAT X DOES
NOT, THEN A IS NOT THAT THING X. AND THIS
IS WHOLE STATEMENT IS NECESSARILY TRUE.
THIS IS BASED ON A PRINCIPLE OF LOGIC WHICH
GOES UNDER VARIOUS NAMES:
SUBSTITUTIVITY OF IDENTITY, LEIBNIZ’S LAW,
INDISCERNIBILITY OF IDENTICALS. “IF
ANYTHING IS TRUE OF A THAT ISN’T TRUE OF
X, THEN X ISN’T A”.

NOW CONSIDER :
(2) IF A HAS PROPERTY P , THEN NECESSARILY: IF
X DOESN’T HAVE P , THEN X IS NOT IDENTICAL
WITH A .”
• THIS MAY SOUND VERY MUCH THE SAME –
THAT’S WHY SOME ABSOLUTE IDEALISTS
CONFUSED THEM.

WITH JUST A LITTLE SYMBOLISM
(FOR THOSE WHO LIKE THAT SORT OF
THING)
(1) [IF A IS P, THEN (IF X IS NOT-P, THEN X A)]
THIS IS TRUE NO MATTER WHAT THINGS X AND A
AND PROPERTY P WE CONSIDER.
(2) [IF A IS P, THEN (IF X IS NOT-P, THEN X A)]
THIS IS NOT TRUE FOR ALL THINGS X AND A AND
PROPERTY P.

THE SECOND DOES NOT FOLLOW
FROM THE FIRST AND IS NOT
GENERALLY TRUE
SUPPOSE THAT YOU ARE A FRIEND OF JONES.
THEN ANYONE X WHO IS NOT FRIEND OF
JONES IS NOT YOU. BUT EVEN IF YOU ARE A
FRIEND OF JONES, YOU MIGHT NOT HAVE
BEEN. IN THAT CASE IT IS NOT TRUE THAT:
NECESSARILY, ANYONE WHO WAS NOT A
FRIEND OF JONES WOULD NOT BE YOU.

HERE IS A SIMPLER CASE OF THE SAME ERROR:
THE SEA BATTLE TOMORROW (ARISTOTLE):
“
IF YOU WILL WIN THE SEA BATTLE TOMORROW,
THEN NECESSARILY YOU WILL WIN
.”
“
IF YOU WILL LOSE THE SEA BATTLE TOMORROW,
THEN NECESSARILY YOU WILL LOSE.”
“
THEREFORE, YOU WILL NECESSARILY WIN OR YOU
WILL NECESSARILY LOSE.” ( FATALISM )

THERE’S NO USE PREPARING, IT IS
ALREADLY NECESSARILY DETERMINED
SOLDIERS IN BATTLE HAVE BEEN KNOWN TO SAY
“IF A BULLET HAS YOUR NAME ON IT, THEN
THAT’S IT. YOU’RE DEAD. IF NOT, YOU’LL BE
O.K.”
I AGREE, BUT YOU SHOULD WEAR YOUR
HELMET ANYWAY.

(3) (IF WILL WIN, THEN WILL WIN)
(4) (IF WILL LOSE, THEN WILL LOSE)
THESE ARE BOTH TRUE, BUT DON’T SAY THAT
THE OUTCOME IS DETERMINED. THE
STATEMENTS NEEDED FOR THAT ARGUMENT
ARE:
(3’) IF WILL WIN, THEN (WILL WIN)
(4’) IF WILL LOSE, THEN (WILL LOSE)
THESE SEEM TO BE FALSE (?)

“IF X AND Y HAVE ALL THEIR QUALITIES IN
COMMON, THEN X IS IDENTICAL WITH Y.”
MAX BLACK’S COUNTEREXAMPLE:

MOORE’S DEFINITION OF “INTERNAL
RELATIONAL PROPERTY” SIMPLIFIED
A
PROPERTY P IS
ESSENTIAL
TO A THING
AND ONLY IF A WOULD HAVE P IN EVERY
A IF
POSSIBLE WORLD IN WHICH IT EXISTED.
A
RELATIONAL PROPERTY P IS
INTERNAL
TO A THING A IF AND ONLY IF P IS
ESSENTIAL TO A .

MOORE POINTS OUT THAT IT IS
EXTREMELY IMPLAUSIBLE TO THINK
THAT ALL RELATIONAL PROPERTIES
ARE INTERNAL (IN HIS SENSE).
IF A IS TEN FEET FROM B , THEN IT DOES NOT
SEEM TO BE ESSENTIAL TO A THAT IT HAVE
THE RELATIONAL PROPERTY OF BEING TEN
FEET FROM B .

ON EITHER OF THESE WAYS OF
DEFINING ‘ INTERNAL RELATION ’, IT
SEEMS THAT THERE ARE EXTERNAL
RELATIONS