William Child - Wittgenstein
Chapter Five - The later philosophy: intentionality and rule-following
2. Rules and Rule-Following
● Wittgenstein’s discussion of rules is influenced by:
○ his refutation of the imagist view of thought - in fact, any picture can be
interpreted in numerous different ways, hence what a picture represents is not intrinsic
but a matter of application
○ his family resemblance theory - our grasp of e.g. ‘game’ depends on the
contingent fact that, having been introduced to the word in various examples, we find it
natural to apply it in new cases in the same way
● Wittgenstein considers two kinds of questions about rules:
○ constitutive questions: what makes it the case that the correct
continuation of the series ‘+2’ is ‘1000, 1002, 1004, 1006’, and not ‘1000, 1004, 1008,
1012’? (accord with the rule)
○ questions bout our knowledge/grasp of rules: what makes it the case that
I have grasped the rule for adding 2? How do I know what I have to do at each
successive step in order to follow the rule?
i. The constitutive question
● Philosophers have tended to answer the constitutive question in two ways:
○ Platonism: it is an absolutely objective fact that the correct continuation
of the series ‘2, 4, 6...996, 998’ is ‘1000, 1002’ etc, and likewise with applying
descriptive words - it is an absolutely objective fact that someone who has been trained in
the normal way to use the word ‘red’ is using it correctly when applied to ripe tomatoes.
This is because the continuation is (absolutely) the simplest or most natural,
■ Wittgenstein rejects Platonism:
● first - there are evidently indefinitely
many possible ways of continuing a series; if we point to something and
say ‘this is called “Boo”’, the word ‘Boo’ might have 10,000 meanings,
none of which is absolutely correct/simplest/most natural
● second - we cannot justify the claim that
our way of continuing is absolutely the correct one. if someone
continues the series ‘1000, 1004, 1008’ then he is not going on in the
same way by our standards, but clearly he is judged by his standards
○ we cannot show that our
standards are absolutely correct
● third - the idea of an absolutely correct
continuation makes no sense. it is not that we can’t tell whether our way
is correct; rather there is no such thing as an absolutely correct
continuation - there are no further facts behind what is most natural by
our standards
○ Constructivism: the correct application of a rule is determined by what
we (would) take to be correct when we (if we were to) consider the case and reach a
, verdict - the fact that we find it natural to continue the series (in normal circumstances at
least) by putting ‘1002, 1004, 1006’ makes that the correct continuation. Normative
claims about correct continuation are underpinned by (but do not mean the same as)
empirical claims about how people actually continue.
■ two big consequences:
● ‘+2’ ceases to be an infinite series. if n
is a number bigger than any human could compute, then there is nothing
to determine what the correct application would be. more generally,
standards of correct application extend no further than our finite capacity
to apply the rule
● there is no standard of correctness
independent of the verdict we reach when we consider the question, so
we must give up the intuitive idea that the truth/falsity of a sentence is
determined by how the world is rather than what we judge when we
consider the matter
○ Deflationism: whereas for the constructivist, Wittgenstein constructs
something normative from something non-normative, for the deflationist he takes facts
about rules and standards of correctness as basic and irreducible. Rules have the features
we ordinarily think they have, so that ‘+2’ really is infinite
■ how we respond is not based on a natural way of going
on (constuctivism), but a rule we are naturally disposed to follow when given e.g.
the series ‘2, 4, 6, 8’
■ the correct continuation is not absolutely the
simplest/most natural (Platonism) but the continuation we find simplest or most
natural, which is a rule
■ deflationism appeals to how we usually understand rules,
and how we explain correct applications to deviant pupils - we take the meaning
of the rule for granted
● Platonism and constructivism both think that philosophy can give a more informative
answer to the question ‘what makes this the correct continuation?’ - they think that there is an
external point of view that we can adopt, whether the nature of numbers/colours (Platonism) or
our nature (constructivism)
○ for the deflationist, the question makes no sense - there is only one
perspective on a practice, and it is internal to that practice
● Deflationism takes Wittgenstein’s anti reductionism seriously - rules/standards of
correctness are seen as basic/fundamental/irreducible
○ but W’s rejection of Goldbach seemed constructivist
ii. Grasping a rule
● How do I know what I have to do at each stage in order to follow a rule? How do I know
to write ‘1000, 1002, 1004’?
○ we can’t rely on any more specific set of instructions because in each
case what counts as following those instructions will be ambiguous/open to interpretation
■ we are tempted to say that in each case there is some
interpretation that is not itself open to interpretation, that is absolute or
unambiguous, and this allows us to follow the rule. but this is a mistake - no
Chapter Five - The later philosophy: intentionality and rule-following
2. Rules and Rule-Following
● Wittgenstein’s discussion of rules is influenced by:
○ his refutation of the imagist view of thought - in fact, any picture can be
interpreted in numerous different ways, hence what a picture represents is not intrinsic
but a matter of application
○ his family resemblance theory - our grasp of e.g. ‘game’ depends on the
contingent fact that, having been introduced to the word in various examples, we find it
natural to apply it in new cases in the same way
● Wittgenstein considers two kinds of questions about rules:
○ constitutive questions: what makes it the case that the correct
continuation of the series ‘+2’ is ‘1000, 1002, 1004, 1006’, and not ‘1000, 1004, 1008,
1012’? (accord with the rule)
○ questions bout our knowledge/grasp of rules: what makes it the case that
I have grasped the rule for adding 2? How do I know what I have to do at each
successive step in order to follow the rule?
i. The constitutive question
● Philosophers have tended to answer the constitutive question in two ways:
○ Platonism: it is an absolutely objective fact that the correct continuation
of the series ‘2, 4, 6...996, 998’ is ‘1000, 1002’ etc, and likewise with applying
descriptive words - it is an absolutely objective fact that someone who has been trained in
the normal way to use the word ‘red’ is using it correctly when applied to ripe tomatoes.
This is because the continuation is (absolutely) the simplest or most natural,
■ Wittgenstein rejects Platonism:
● first - there are evidently indefinitely
many possible ways of continuing a series; if we point to something and
say ‘this is called “Boo”’, the word ‘Boo’ might have 10,000 meanings,
none of which is absolutely correct/simplest/most natural
● second - we cannot justify the claim that
our way of continuing is absolutely the correct one. if someone
continues the series ‘1000, 1004, 1008’ then he is not going on in the
same way by our standards, but clearly he is judged by his standards
○ we cannot show that our
standards are absolutely correct
● third - the idea of an absolutely correct
continuation makes no sense. it is not that we can’t tell whether our way
is correct; rather there is no such thing as an absolutely correct
continuation - there are no further facts behind what is most natural by
our standards
○ Constructivism: the correct application of a rule is determined by what
we (would) take to be correct when we (if we were to) consider the case and reach a
, verdict - the fact that we find it natural to continue the series (in normal circumstances at
least) by putting ‘1002, 1004, 1006’ makes that the correct continuation. Normative
claims about correct continuation are underpinned by (but do not mean the same as)
empirical claims about how people actually continue.
■ two big consequences:
● ‘+2’ ceases to be an infinite series. if n
is a number bigger than any human could compute, then there is nothing
to determine what the correct application would be. more generally,
standards of correct application extend no further than our finite capacity
to apply the rule
● there is no standard of correctness
independent of the verdict we reach when we consider the question, so
we must give up the intuitive idea that the truth/falsity of a sentence is
determined by how the world is rather than what we judge when we
consider the matter
○ Deflationism: whereas for the constructivist, Wittgenstein constructs
something normative from something non-normative, for the deflationist he takes facts
about rules and standards of correctness as basic and irreducible. Rules have the features
we ordinarily think they have, so that ‘+2’ really is infinite
■ how we respond is not based on a natural way of going
on (constuctivism), but a rule we are naturally disposed to follow when given e.g.
the series ‘2, 4, 6, 8’
■ the correct continuation is not absolutely the
simplest/most natural (Platonism) but the continuation we find simplest or most
natural, which is a rule
■ deflationism appeals to how we usually understand rules,
and how we explain correct applications to deviant pupils - we take the meaning
of the rule for granted
● Platonism and constructivism both think that philosophy can give a more informative
answer to the question ‘what makes this the correct continuation?’ - they think that there is an
external point of view that we can adopt, whether the nature of numbers/colours (Platonism) or
our nature (constructivism)
○ for the deflationist, the question makes no sense - there is only one
perspective on a practice, and it is internal to that practice
● Deflationism takes Wittgenstein’s anti reductionism seriously - rules/standards of
correctness are seen as basic/fundamental/irreducible
○ but W’s rejection of Goldbach seemed constructivist
ii. Grasping a rule
● How do I know what I have to do at each stage in order to follow a rule? How do I know
to write ‘1000, 1002, 1004’?
○ we can’t rely on any more specific set of instructions because in each
case what counts as following those instructions will be ambiguous/open to interpretation
■ we are tempted to say that in each case there is some
interpretation that is not itself open to interpretation, that is absolute or
unambiguous, and this allows us to follow the rule. but this is a mistake - no
