Ranil
Sandanayake
ID: 95146937
November 6,
2001
PHIL
473/673
Robert
Cummins’ Representations, Targets and Attitudes
Desiderata: something desired as essential
(Merriam-Webster’s Collegiate Dictionary)
-
The
conception of representational content should be:
1.
Distinct
from targets
Ø
Error is a
mismatch between the content of a representation and the target of a particular
application of it. (p. 85)
2.
Distinct
from attitude content
Ø
Attitude
content = application content
= representational content applied to target (p. 85-86)
3.
Independent
of use or functional role
Ø
There is
no room for error if by using “r to represent t” makes “r a representation of
t”. (p. 86)
4.
Neither
holistic nor atomistic
Ø
Some
schemes of representation are holistic and others are not. Thus it can’t be a property of meaning that
it is holistic or atomistic. (p. 86)
*knowledge: what philosophers normally call belief. This term is used in psychology and artificial intelligence. I can be neither true nor justified, and it need not be conscious or accessible to consciousness.
Meaning: a two-place relation between a representation and a content
Meaningfor: a three-place relation between a representation, a concept and a cognitive system
- meaning is a semantic notion; meaningfor is a cognitive notion.
- “If (representation) R means elevator, that is, represents the property of being an elevator, then R’s meaningfor me ought to be my *knowledge of elevators.” (p. 87)
- the distinction between meaning and meaningfor is obscured by ambiguity in the use of the word ‘concept’
- Concept of elevator is:
1. My cognitive grip on elevators, a cognitive structure that is, or at any rate, organizes my *knowledge of elevators
2. A mental representation – an |elevator|
- Number (1) is the majority view on concepts in psychology. See elevator example (p. 88) and Figure 7.1 (p. 89)
- Result: One can have a concept of elevator without a mental representation.
- Concepts are knowledge structures. Knowledge structures are organized attitudes, NOT mental representations
- A sloppy use of ‘concept’ assimilates mental representations to knowledge structures, and hence assimilates meaning to meaningfor
- Our target is meaning, not meaning for
The Picture Theory: Preview
Definition
Isomorphism: a
one-to-one correspondence between two mathematical sets
Cummins’ theory
of representational content:
1. Representation is an isomorphic relation
between two structures
-
things
whose semantic properties are not grounded in isomorphism have meaningfor but
not meaning
2. Only structures represent, since only
structures can be related by isomorphism
3. Mental representation is representation
grounded in isomorphism
4. Construing mental representation in
terms of isomorphism underwrites the explanatory role of mental representation
in contemporary theories of cognition.
ISOMORPHISM AND
COGNITIVE EXPLANATION
-
Representations
would have a clear explanatory role if they could be thought of as proxies for
the things they represent
-
See
historical fable, p. 91 to p. 92, from Aristotelian science to “good
old-fashioned AI” (GOFAI)
-
GOFAI is
this: representations and rules and the computing machinery are in each of our
heads.
-
Transformations
effected on the representations by internal computations must mirror
transformations effected by nature on what is represented
-
So, our
inner psychological states better be isomorphic
to the outer world
-
When this
happens, “a representation r in the head is a proxy or representative to the
mind of the thing represented” (p. 92) because it behaves inside the head in an
analogous way to how things behave outside in nature
-
Computational
laws govern the behaviour of the representation in the mind, just as the laws
of nature govern what is being represented
-
This story
motivates Cummins’ account that he gave in Meaning
and Mental Representation
-
But that
story is no good because it is a use theory, a version of CRS (see critique in
chapter 4)
-
The
Picture Theory of Representation (PTR) holds the idea of representations as
proxies while avoiding CRS
-
It does
this by holding that representations are isomorphic to what they represent,
“while rejecting the idea that it is the mind’s processing that structures the
relations between elements in a representation” (p. 93)
-
Cummins
considers the map example from chapter 5:
“the blocks stand to the spaces between them as the buildings stand to
the streets, and this is what makes it possible to assess the accuracy of a map
independently of how it is used.” (p. 93)
-
Cummins
calls this kind of meaning intrinsic
-
Since maps
are isomorphic of the things they map, then the blocks can be seen as proxies
or representatives of the buildings, the spaces between the blocks are proxies
of the streets
-
Isomorphs
share structure, so the idea behind PTR is that to represent something is to
have its structure
-
Now
Cummins uses the distinction of intrinsic meaning that he made with the maps:
-
“The
structure that is crucial to cognitive explanation is extrinsic to symbols, but
internal to such things as maps.” (p. 93)
-
symbols
are in the communication business while maps are in the representation business
-
reference
isn’t representation
-
The
Autobot example (from now on the Autobot will be referred to as Optimus Prime!) page 94 and Figure 7.2
-
The moral
of the story is that such a card would be a map of the maze, or an
isomorphism. We understand why meaning
matters without identifying meaning with functional role because the representation
is just as good as sensing the environment
-
PTR also
deals with the problem of knowing a changing world (which motivated the
historical fable previously), because you can represent change or dynamics in
the structure of the representation, instead of changing the representations
you have.
PTR is good:
-
We can see
our way clear to an account of how it satisfies the Explanatory Constraint
-
It makes
meaning independent of use
-
It does
not threaten a confusion of representational contents with targets or with
attitude contents
-
The
representation relation is just the relation of isomorphism
-
The idea
of an isomorphism is that it is a mapping between two structures such that:
1. For every object in the content
structure C, there is exactly one corresponding object in the representing
structure R
2. For every relation defined in C, there
is exactly one corresponding relation defined in R
3. Whenever a relation defined in C holds
of an n-tuple of objects in C, the corresponding relation in R holds on the
corresponding n-tuple of objects in R
If a structure
R represents a structure C, then
1. An object in R can represent an object
in C.
2. A relation in R can represent a relation
in C.
3. A state of affairs in R – a relation
holding of an n-tuple of objects – can represent a state of affairs in C.
-
Things in
R represent things in C because R is isomorphic to C.
-
“PTR
entails that every genuinely representational scheme is molecular in that the
meaningful constituents of a structure are meaningful only in the context of
some structure or other.” (p. 97)
-
A problem
facing PTR is that isomorphisms are not unique
-
To see why
this is a problem, recall Optimus Prime.
If the card was put in upside down, then we still have an isomorphism,
because the turns are all inverted, but we don’t have a correct path
-
The
invited conclusion is that specifying the content of a representation requires
specifying a particular isomorphism.
But this abandons the idea that the content of a representation is
intrinsic and independent of its use
-
This is a
serious problem: If we say that
specifying the content of a representation does not require specifying a
particular isomorphism, the we will b left with no determinate notion of error. But no determinate notion of error implies
no determinate notion of content. If we
say that specifying the content of the representation does require specifying a particular isomorphism, then this implies
that use determines content.
What is the
solution?
-
Cummins
notes that turning the card upside down does not change its representational
content, all it changed was how Optimus Prime used the representation. “If your map is not properly oriented, you
won’t get to your destination, but that
is not the map’s fault.” (p. 99)
-
Also,
elements of a representing structure should not be thought of as independent
semantic constituents. The portion of
the slit in Figure 7.3 represents a left turn when the card is inserted
correctly, and a right turn when it is inserted upside down, and various other
things with other isomorphisms. You
must look at the whole structure first, determine what it represents, and then
infer what its parts correspond to.
-
The fact
that the target is among the things that the card represents explains, in part, why the car succeeds. Representational correctness isn’t enough to
explain success, for example a picture of the maze is completely useless to
Optimus Prime.
-
Also
attitudes that have the same content does not imply that they have the same
state, as we see that the card used in two different ways shares the attitude
that there is a free path through the maze.
-
The idea
that a printed picture of the maze is unusable to Optimus Prime, might lead to
the conclusion that representational content is relative to the user
-
Cummins
claims that this is the confusion between meaningfulness and meaningforness.
-
Recall: we
want to explain meaningfor in terms of meaning, where meaning is a semantic
notion and meaningfor is not.
-
Thus we
shouldn’t focus on what the slitted card meansfor
Optimus Prime. In the case of the
upside down card and the printed picture, the meaning is there, but Optimus
Prime cannot exploit it.
-
One should
not confuse this question with an analogy to what a map communicates to someone
who cannot read it properly. The
Optimus Prime question is one about internal representation, and not about
communication or understanding
-
“A system
exploits an internal representation in the way a lock exploits a key: by being
causally affected by its structure.” (p. 102)
-
The
non-uniqueness of isomorphic representation does not undermine its explanatory
value because the explanatory work is done by the match (or mismatch) between
content and target.
-
Cummins
draws further distinction between what something communicates and what it
represents
-
See the
two-case map example (p. 103)
-
Representational
content is not a function of its communicative content
-
“We cannot
suppose that mental representations are in the communications business without
undermining the goal of explaining cognitive capacities in terms of the
capacity to represent.” (p. 104)
-
PTR cannot
represent the difference between left-handed and right-handed gloves
-
But, this
does not pose a problem, because left and right can still be known, and you can
still have a concept of this, but this is in the meaningfor sense, and not the
meaning sense.
-
A
representational theory needs to explain how error can come in degrees. This seems to be a problem for PTR
-
To get a
graded notion of accuracy it would seem that PTR needs to define a “partial”
isomorphism. This should be avoided!
-
What is
required is the notion of how similar two structures are alike.
-
Cummins
does not know whether this approach can work, but gives examples on page 108 to
convince us that shared structure is plausible
Targets and Structures
-
targets
differ from content in one important respect, targets are structures of
something, whereas contents are simply structures
-
Which
something is typically fixed indexically (see Chess example, last paragraph of
section on page 110)
Structural Representation