Baker and Hacker - Wittgenstein: Rules, Grammar and Necessity
Chapter Three: Accord with a rule
1. Initial compass bearings
● What questions was Wittgenstein addressing, and why did he see any need to address
them?
○ what justifies our verdict that 1002 is the next term, following 1000,
according to the rule ‘+2’?
■ not intuition, unless the mind could ‘traverse the entire
series of even integers in a flash’
■ is it the formula? how can a mere expression determine
what is correct/incorrect?
■ is it the rule itself - not the formula?
● this seems to rely on a Platonic
mechanism that generates consequences independently of us
■ is it justified by an interpretation? but there can be many
interpretations that give different accounts of what is correct/incorrect (Kripke)
● We can understand an expression yet explain it incorrectly, and we can explain an
expression correctly yet misapply it, so it is important to see how explanation and use are related
○ it is also difficult to talk of someone understanding a word where
meaning is use, because use spreads over time. are future uses already present in the rule
for its use?
■ explanations function as standards for determining
correct use - hence they are rules for use. so we must analyse rules to understand
all this shit
2. Accord and the harmony between language and reality
● Starting point: if one understands a rule, one knows what to do in order to act in
accordance with it
○ this is like W’s 1930s preoccupation with the relation between a desire
and its realization - does a desire contain a state of affairs, a picture of a state of affairs, or
what?
○ the relation between these things is internal
■ a property is internal if it is unthinkable that its bearer
should not possess it - a relation is internal if it is unthinkable that these two
objects should not stand in this relation i.e. these properties/relations are partly
constitutive of the natures of the things whose attributes they are
● Post-Tractatus, W moved from an interest in the relationship between a proposition and
its negation to that between belief and its validation, expectation and its fulfilment etc
○ expectation and fulfilment use the same symbol
■ i.e. if i expect that p, then the fulfilment of that
expectation cannot be described without using p
■ the relation between a belief and what makes it true is
formed in language
● this (and the previous discussion) is an
, analogue for rules
● How can a rule determine in advance what accords with it, without containing its
extension? What makes the rule and the according act agree with each other?
○ Tractatus - rule contains ‘in some sense’ a picture of what accords with it
■ ‘shadowy intermediary’
○ Russell - the rule doesn’t determine what is in accord with it (community
view)
■ intermediary + denial of the internal relation
○ Wittgenstein - the internal relation
■ it is true that an F’s V-ing in circumstances C is an act
that accords with the rule that Fs should V in C
■ the rule wouldn’t be the rule it is, (OR?) the act wouldn’t
be the act that it is, if the act didn’t count as being in accord with the rule
● the internal relation precludes any
intermediary (really? is the ‘picture’ of the Tractatus not an intermediary,
with the relation remaining internal?
■ 1002 follows 1000 because the rule and its extension are
not two things that can be grasped independently of one another
● the rule would not be the rule it is were
1000 followed by any other number
3. Rules of inference and logical machinery
● Is it not the case that all rules are mediated through a logical principle of universal
instantiation - i.e. ‘From (x)fx infer fa’? In other words, our ability to accord and conflict with
the rule seems to be grounded in the laws of logic (c.f. Winch - Achilles and the Tortoise. don’t
we need an additional principle? e.g. ‘from ‘From (x)fx infer fa’ and (x)fx, infer fa’)
○ but how can the laws of logic be essential to relate propositions that are
already intrinsically, internally related?
● Inferring is a human activity - we say that someone has inferred such-and-such if the
expression of what he has inferred is a transformation of other propositions according to a
paradigm
○ the rules of inference are partly constitutive of the meaning of logical
language e.g. part of the meaning of ‘negation’
■ this means that an inference rule cannot make
connections between internally related propositions - rules of inference are only
essential to the explanations of the meanings of logical operators (seems highly
implausible. why wouldn’t accordance with a rule rest on acknowledgement of
universal instantiation?
■ a rule of inference doesn’t ‘engineer a fit’ between
independently given propositions, but ‘makes perspicuous the fact that a pair of
propositions belong to one another, that they are internally related.’
4. Formulations and explanations of rules by examples
● Sometimes we explain a rule by giving a set of examples, which can function as the
expression of a rule e.g. ‘0, 2, 4, 6, 8’, or family resemblance concepts
○ but a set of examples such as this can accord with any number of
Chapter Three: Accord with a rule
1. Initial compass bearings
● What questions was Wittgenstein addressing, and why did he see any need to address
them?
○ what justifies our verdict that 1002 is the next term, following 1000,
according to the rule ‘+2’?
■ not intuition, unless the mind could ‘traverse the entire
series of even integers in a flash’
■ is it the formula? how can a mere expression determine
what is correct/incorrect?
■ is it the rule itself - not the formula?
● this seems to rely on a Platonic
mechanism that generates consequences independently of us
■ is it justified by an interpretation? but there can be many
interpretations that give different accounts of what is correct/incorrect (Kripke)
● We can understand an expression yet explain it incorrectly, and we can explain an
expression correctly yet misapply it, so it is important to see how explanation and use are related
○ it is also difficult to talk of someone understanding a word where
meaning is use, because use spreads over time. are future uses already present in the rule
for its use?
■ explanations function as standards for determining
correct use - hence they are rules for use. so we must analyse rules to understand
all this shit
2. Accord and the harmony between language and reality
● Starting point: if one understands a rule, one knows what to do in order to act in
accordance with it
○ this is like W’s 1930s preoccupation with the relation between a desire
and its realization - does a desire contain a state of affairs, a picture of a state of affairs, or
what?
○ the relation between these things is internal
■ a property is internal if it is unthinkable that its bearer
should not possess it - a relation is internal if it is unthinkable that these two
objects should not stand in this relation i.e. these properties/relations are partly
constitutive of the natures of the things whose attributes they are
● Post-Tractatus, W moved from an interest in the relationship between a proposition and
its negation to that between belief and its validation, expectation and its fulfilment etc
○ expectation and fulfilment use the same symbol
■ i.e. if i expect that p, then the fulfilment of that
expectation cannot be described without using p
■ the relation between a belief and what makes it true is
formed in language
● this (and the previous discussion) is an
, analogue for rules
● How can a rule determine in advance what accords with it, without containing its
extension? What makes the rule and the according act agree with each other?
○ Tractatus - rule contains ‘in some sense’ a picture of what accords with it
■ ‘shadowy intermediary’
○ Russell - the rule doesn’t determine what is in accord with it (community
view)
■ intermediary + denial of the internal relation
○ Wittgenstein - the internal relation
■ it is true that an F’s V-ing in circumstances C is an act
that accords with the rule that Fs should V in C
■ the rule wouldn’t be the rule it is, (OR?) the act wouldn’t
be the act that it is, if the act didn’t count as being in accord with the rule
● the internal relation precludes any
intermediary (really? is the ‘picture’ of the Tractatus not an intermediary,
with the relation remaining internal?
■ 1002 follows 1000 because the rule and its extension are
not two things that can be grasped independently of one another
● the rule would not be the rule it is were
1000 followed by any other number
3. Rules of inference and logical machinery
● Is it not the case that all rules are mediated through a logical principle of universal
instantiation - i.e. ‘From (x)fx infer fa’? In other words, our ability to accord and conflict with
the rule seems to be grounded in the laws of logic (c.f. Winch - Achilles and the Tortoise. don’t
we need an additional principle? e.g. ‘from ‘From (x)fx infer fa’ and (x)fx, infer fa’)
○ but how can the laws of logic be essential to relate propositions that are
already intrinsically, internally related?
● Inferring is a human activity - we say that someone has inferred such-and-such if the
expression of what he has inferred is a transformation of other propositions according to a
paradigm
○ the rules of inference are partly constitutive of the meaning of logical
language e.g. part of the meaning of ‘negation’
■ this means that an inference rule cannot make
connections between internally related propositions - rules of inference are only
essential to the explanations of the meanings of logical operators (seems highly
implausible. why wouldn’t accordance with a rule rest on acknowledgement of
universal instantiation?
■ a rule of inference doesn’t ‘engineer a fit’ between
independently given propositions, but ‘makes perspicuous the fact that a pair of
propositions belong to one another, that they are internally related.’
4. Formulations and explanations of rules by examples
● Sometimes we explain a rule by giving a set of examples, which can function as the
expression of a rule e.g. ‘0, 2, 4, 6, 8’, or family resemblance concepts
○ but a set of examples such as this can accord with any number of
