Saul Kripke - Wittgenstein on Rules and Private Language
The Wittgensteinian Paradox
● Wittgenstein says ‘this was our paradox: no course of action could be determined by a
rule, because every course of action can be made to accord with the rule’
○ very important, and a new form of philosophical scepticism
● There is no rule that can apply to all experience, present and past, or infinitely many
situations
○ this is because, even if we look as past usage, the rule has only been
applied a finite number of times, and hence any present application will be consistent
with past usage
■ e.g. imagine someone who has only done additions using
numbers smaller than 57. they add 57 and 65, and think the answer is 125. but
for all we (or anyone/God) know, they may have been practicing quaddition,
which states that numbers up to 57 are added ‘normally’, but numbers 57 and
highers, when ‘quadded’, always equal 5.
● this is logically possible
● hence we think we have been adding,
but really we have been quadding (a practice which is consistent with all
past usage)
● An answer to the sceptic must satisfy two conditions:
○ it must state what fact about my mental state constitutes my meaning
plus
○ it must show how I am justified in giving the answer ‘125’ to ‘57 + 65’
■ the directions must be contained in the fact as to what I
meant
● If the sceptic is right, the concepts of meaning and intending one function rather than
another will be meaningless
○ if there can be no fact about which particular function was meant in the
past, there can be no fact about which particular function is meant in the present
■ these facts may be internal or external (i.e. from within
the mind or behaviourist)
● If we are asked to continue the sequence ‘2, 4, 6, 8’ the answer may be 10, or may be 45,
or indeed anything
○ this is because the ‘rule’ of the sequence may, for all we know, imply a
different spacing after 8
■ even if the series is called ‘+2’ this is still a problem,
because +2 can be interpreted and reinterpreted
● ‘This, then, is the sceptical paradox. When I respond in one way rather than another to
such a problem as ‘68 + 57’, I can have no justification for one response rather than another.
Since the sceptic who supposes that I mean quus cannot be answered, there is no fact about me
that distinguishes between my meaning plus and my meaning quus. Indeed, there is no fact about
me that distinguishes between my meaning a definite function by plus (which determined my
responses in new cases) and my meaning nothing at all.’
The Wittgensteinian Paradox
● Wittgenstein says ‘this was our paradox: no course of action could be determined by a
rule, because every course of action can be made to accord with the rule’
○ very important, and a new form of philosophical scepticism
● There is no rule that can apply to all experience, present and past, or infinitely many
situations
○ this is because, even if we look as past usage, the rule has only been
applied a finite number of times, and hence any present application will be consistent
with past usage
■ e.g. imagine someone who has only done additions using
numbers smaller than 57. they add 57 and 65, and think the answer is 125. but
for all we (or anyone/God) know, they may have been practicing quaddition,
which states that numbers up to 57 are added ‘normally’, but numbers 57 and
highers, when ‘quadded’, always equal 5.
● this is logically possible
● hence we think we have been adding,
but really we have been quadding (a practice which is consistent with all
past usage)
● An answer to the sceptic must satisfy two conditions:
○ it must state what fact about my mental state constitutes my meaning
plus
○ it must show how I am justified in giving the answer ‘125’ to ‘57 + 65’
■ the directions must be contained in the fact as to what I
meant
● If the sceptic is right, the concepts of meaning and intending one function rather than
another will be meaningless
○ if there can be no fact about which particular function was meant in the
past, there can be no fact about which particular function is meant in the present
■ these facts may be internal or external (i.e. from within
the mind or behaviourist)
● If we are asked to continue the sequence ‘2, 4, 6, 8’ the answer may be 10, or may be 45,
or indeed anything
○ this is because the ‘rule’ of the sequence may, for all we know, imply a
different spacing after 8
■ even if the series is called ‘+2’ this is still a problem,
because +2 can be interpreted and reinterpreted
● ‘This, then, is the sceptical paradox. When I respond in one way rather than another to
such a problem as ‘68 + 57’, I can have no justification for one response rather than another.
Since the sceptic who supposes that I mean quus cannot be answered, there is no fact about me
that distinguishes between my meaning plus and my meaning quus. Indeed, there is no fact about
me that distinguishes between my meaning a definite function by plus (which determined my
responses in new cases) and my meaning nothing at all.’
