Systematicity and Cognitive Architecture

About This Presentation

Title:

Systematicity and Cognitive Architecture

Description:

Systematicity and Cognitive Architecture In Connectionism and Cognitive Architecture: A Critical Analysis (1988), Fodor and Pylyshyn pose several challenges for ... – PowerPoint PPT presentation

Number of Views:106

Avg rating:3.0/5.0

Slides: 138

Provided by: Philos3

Category:

more less

Transcript and Presenter's Notes

Title: Systematicity and Cognitive Architecture

1
Systematicity and Cognitive Architecture

In Connectionism and Cognitive Architecture A
Critical Analysis (1988), Fodor and Pylyshyn
pose several challenges for any connectionist
theory of cognitive architecture.

2
The Systematicity Challenge

One is to explain the systematicity of thought
without implementing a classical cognitive
architecture.

3
The Language of Thought (LOT)

By a classical cognitive architecture they mean
a Language of Thought (LOT) architecture.

A LOT architecture includes a mental symbol
system with a compositional semanticsso that the
semantic value of a molecular mental symbol is a
function of the semantic values of the atomic
mental symbols that are its constituents together
with the syntactic structure of the molecular
symbol, and includes computational operations
that molecular symbols participate in in virtue
of their syntactic and other formal properties.

By the LOT hypothesis, lets mean the hypothesis
that the cognitive architecture of beings with
the ability to think includes a kind of LOT
architecture.

6
A Dilemma

The systematicity challenge presents a dilemma.
If connectionism cannot explain the systematicity
of thought, then it fails to offer an adequate
theory of cognitive architecture and
if it explains the systematicity of thought by
implementing a LOT architecture, then it fails to
offer an alternative to the LOT hypothesis.

Given that thought is systematic, connectionism
can offer an adequate alternative to the LOT
hypothesis only if it can meet this challenge.

8
Critical Reaction

Critical reaction to the challenge was divided.
Some critics tried to meet the challenge.
Some argued that it need not be met since thought
is not in fact systematic.
And some claimed not to even understand the claim
that thought is systematic.

What Ill do today is defend the challenge by
explicating the notion of systematicity in a way
that I hope makes clear that thought is indeed
systematic.

In their 1988 paper, Fodor and Pylyshyn claim
both that thoughts and that linguist abilities
are systematic, but they did not state
non-circular necessary and sufficient conditions
for the property of being systematic nor has
either of them offered such in any subsequent
works.

11
A Complaint

Matthews (1994), Niklasson and van Gelder (1994),
van Gelder and Niklason (1994), Hadley (1997),
Johnson (2004) and others have complained about
the lack of a definition of systematicity.

12
No Definition

I think that no definition is to be had.

However, that is no objection to the
systematicity challenge.
How often can something a scientific theory is
challenged to explain be characterized by
non-circular necessary and sufficient conditions?

Still the locution the systematicity of thought
is a technical one, and the absence of a
definition has led to much speculation about what
the claim that thought is systematic means.

Ill now begin to spell that out.
Then, I will discuss a misguided attempts to
spell the thesis out by Kent Johnson (2004).
Ill conclude with an explication of the
systematicity challenge.

16
Issue Not Computational Power

It should be noted first of all that the
systematicity challenge is not generated by
skepticism about the computational powers of
multi-layered connectionist networks.

Such networks are Turing-equivalent.
Computational power is thus not the issue.
The challenge is thus not, as some respondents
have mistakenly thought (e.g., Chalmers 1990), to
show that a connectionist network can compute
certain functions, such as, for instance,
linguistic functions.

Further, as is not doubt already obvious from how
the systematicity challenge is stated,
implementational connectionism is not at issue.
(It is worth noting that Turing machines and
production systems have been implemented by
connectionist architectures.)

19
Explaining Laws

The challenge is, rather, generated by skepticism
about the prospects for explaining certain
psychological laws by appeal to a connectionist
architecture that does not implement a LOT
architecture.

By a psychological law I mean here simply a
psychological generalization that is true (at
least ceteris paribus) and counterfactual
supporting.
Explaining the systematicity of thought is just
matter of explaining the psychological laws in
question.

21
Systematicity Laws

Lets call the laws in question systematicity
laws.
The thesis that thought is systematic amounts to
the thesis that there is a family of
systematicity laws.
The task of characterizing the systematicity of
thought is thus that of saying what laws are
systematicity laws.

Systematicity laws are correlation laws.
They assert the co-possession of the members of
certain pairs of thought abilities.
They are all laws to the effect that ceteris
paribus, a cognizer has a certain thought ability
if and only if the cognizer has a certain other
thought ability.

The thought abilities in question are abilities
to think certain thoughts.
There are, however, no non-circular necessary and
sufficient conditions for a pair of abilities to
think certain thoughts being one of the pairs in
question as least none that would not be
regarded by some as question-begging in the
present dialectical context and so there are no
non-circular necessary and sufficient conditions
for being a systematicity law.

But I think that enough can be said by way of
indicating the sorts of laws in question for the
purpose of posing the systematicity challenge.
Of that, more later.

25
Productivity of Thought

Fodor and Pylyshyn (1988) pose the systematicity
challenge after posing the productivity
challenge the challenge to explain the
productivity of thought by appeal to a
connectionist architecture that does not
implement a LOT architecture.
The claim that thought is productive is the claim
that a thinker is, in principle, able to think an
unbounded number of thoughts.

26
Constituent Structures

Fodor and Pylyshyn press the productivity
challenge to make apparent the need to postulate
mental representations with constituent
structures.

27
Idealization

But the claim that thought is productive involves
idealization.
A human, being a finite creature, cant actually
think an unbounded number of thoughts.

Acknowledging that some connectionists (e.g.,
Rumelhart and McClelland (1986, p. 191)) reject
idealizations to unbounded cognitive abilities,
Fodor and Pylyshyn claim that appeal to the
systematicity of thought, which involves no such
idealization, suffices to make the case that
mental representations have constituent
structures.

The idea of thought-productivity is that any
being able to have a thought would in principle
be able to have an unbounded number of thoughts.
The kernal of the idea that thought is systematic
is that any being able to have a thought would be
able to have a family of other thoughts, whose
members have related (though non-equivalent)
contents.

Abilities to have thoughts come in clusters, so
that there are no cognizers with punctuate
thought abilities or the ability to think, say,
27 semantically unrelated thoughts.

The idea that thought abilities come in clusters
can be captured by saying that they come in
pairs, where it is understood that a given
thought ability can be a member of more than one
pair.
The pairs are such that ceteris paribus, a
cognizer has one member if and only if the
cognizer has the other.

32
A Paradigm

A paradigm example from the literature of a pair
of systematically related thought abilities is
the ability to think the thought that John loves
Mary and the ability to think the thought that
Mary loves John.
One can of course think that John loves Mary
without thinking that Mary loves John.
But the idea is that ceteris paribus, anyone able
to think the one thought would be able to think
the other.

33
A Schema

This idea can be generalized by appeal to a
predicate logic sentence schema Ceteris
paribus, a cognizer is able to think the thought
that aRb if and only if the cognizer is able to
think the thought that bRa.
The claim is that generalizations that are
instances of this schema are true and
counterfactual supporting, and so are in that
sense psychological laws.
Instances of this schema are members the family
of systemacity laws, and so are among the
psychological laws that connectionism is being
challenged to explain.

Other laws of systematicity are, like the
instances of this of schema, quite low-level
laws.
They all specify what it is the thought abilities
they cite are abilities to think, rather than
quantifying over what the thought abilities are
abilities to think.
They are laws, to repeat, in the sense that they
are true, counterfactual supporting
generalizations.

35
Strategy

I have here employed a strategy common in the
literature for identifying systematicity laws.
The strategy is to identify them by appeal to
sentence schemata the instances of which are
systematicity laws.

In their 1988 paper, Fodor and Pylyshyn appealed
to a schema only once in their discussion of the
systematicity of thought (p.30).

But schemata are widely used elsewhere in the
literature on systematicity see, for example,
McLaughlin (1987), Fodor and McLaughlin (1990),
Fodor and Lepore (1992), McLaughlin (1993a),
(1993b), (1997), and Aizawa (2003).
I will state further such schemata later.

I have here also followed Fodor and Pylyshyns
practice of characterizing the thought abilities
in question as abilities to think certain
thoughts.

Use of the locution think the thought that has,
however, led to misunderstandings in some
quarters.
This expression suggests the ability to
occurently think something or to believe
something.
But in fact that is not what is intended.

40
Representational Theory of Mind

Fodor and Pylyshyn embrace a representational
theory of mind.
According that theory, believing that p,
occurrently thinking that p, desiring that p,
intending that p, imagining, hoping, wishing,
fearing, considering whether p, as well as simply
entertaining the thought that p, all involve
mentally representing that p.

By think the thought that p Fodor and Pylyshyn
mean mentally represent that p.
And they take mentally representing that p to
involve having a mental representation that means
that p.
What makes the type of representation in question
a mental representation is that it can function
in the cognizers cognitive economy in such a way
that its content is the content of a
propositional attitude of the cognizer.

The relevant thought abilitiesthe ones that are
systematically related, related by systematicity
lawsare thus abilities to have mental
representations with propositional contents
(contents expressible by that-clauses) that are
the contents of propositional attitudes the
cognizer is able to have.

Failure to appreciate that thinks the thought
that is to be understood as mentally represent
that has led to some misguided objections to the
schema stated earlier, namely
Ceteris paribus, a cognizer is able to think
the thought that aRb if and only if the cognizer
is able to think the thought that bRa.

Matthews (1994) claims that someone can think
that x is the sole member of x yet be unable to
think that x is the sole member of x.
Here think that is used to mean believe that
(or occurrently think that), rather than to mean
mentally represent that.

But given how thinks the thought that is to be
understood, the relevant schema is actually this
Ceteris paribus, anyone able to mentally
represent that aRb is able to mentally represent
that bRa.

Even where Tom is, say, the name of a person,
the sentence Ceteris paribus, a cognizer is able
to mentally represent that Tom is the sole member
of Tom if and only if the cognizer is able to
mentally represent that Tom is the sole member
of Tom is an instance of this schema.
And that generalization is true and
counterfactual supporting.

One mentally represents that Tom is the sole
member of Tom when one disbelieves that Tom is
the sole member of Tom (perhaps taking it to be
necessarily false that Tom even has members in
the sense in question).
Disbelief differs of course from non-belief.
One disbelieves that p if and only if one
believes that not-p.

Given the reading that thinks the thought that
naturally invites, the misunderstanding in
question is perhaps understandable (though I
believe that typically surrounding texts in the
relevant literature should have made the intended
interpretation clear).
As well see later, however, some other
misunderstandings of such schemata in the
literature are harder to understand, and seem to
be the result of misunderstandings of how
schemata are used.

Connectionists that deny that there are mental
representations will of course reject the
systematicity challenge on the grounds that there
are no mental representations to be
systematically related.

But the systematicity challenge is aimed at
connectionists that posit mental representations,
whether they take a mental representation to be
an activated unit in a connectionist network (and
so local) or instead to be a pattern of
activation over a groups of units in a network
(and so distributed).

The systematicity challenge is thus aimed at
connectionists that are realists about mental
representations, not at connectionists that are
eliminativists about mental representations.

The main challenge to eliminativist connectionism
is different.
It is to provide an adequate theory of cognition
without positing mental representations.
But Ill say no more about that issue.

53
Intrinsic Connections

Although Fodor and Pylyshyn (1988) offer no
canonical formulation of the general thesis that
thought is systematic, one way they characterize
systematicity is in terms of intrinsic
connections among thought abilities.
Their idea seems to be that thought abilities
come in clusters because members of the clusters
are intrinsically connected.

Some critics regard appeal to intrinsic
connections among thought abilities in the very
characterization of systematicity as
question-begging in the context of the
connectionism/LOT debate (Matthews 1994).

On a natural reading of intrinsically related,
what it is for thought abilities to be
intrinsically related is for them to be complex
abilities that are constituted by some of the
same abilities.

56
Conceptual Abilities

The natural suggestion is that the abilities in
question are conceptual abilities.
The ability to think that John loves Mary and the
ability to think that Mary loves John both
involve the ability to think about Mary, the
ability to think about John, and the ability to
think about one individual loving another.
These are conceptual abilities.

57
Constitution

The intrinsic relatedness idea thus seems to be
that the thought abilities in question are
constituted by conceptual abilities.

Given that thinking the thought that p is to be
understood as mentally representing that p and
that thinking about X is to be understood as
mentally representing X, the intrinsic
relatedness idea thus seems to be that the
ability to mentally represent that John loves
Mary and the ability to mentally represent that
Mary loves John both consist in the ability to
represent Mary, the ability to represent John,
the ability to represent one individual as loving
another, and a second-order conceptual ability to
jointly exercise these abilities to represent
that John loves Mary and to represent that Mary
loves John.

This has raised the concern that the very claim
that thought is systematic presupposes that there
is a system of mental representation that is a
language of thought (Matthews 1994).
The systematicity challenge is posed for
connectionists that posit a system of mental
representation.
But the concern is that if such connectionists
concede that thought is systematic in the sense
in question, they would in effect be conceding
that the system of mental representation is a LOT.

60
The Conceptual Constitution Thesis

Let us call the thesis that abilities to think
thoughts are constituted by conceptual abilities
the conceptual constitution thesis.

In their intrinsic connection discussion, Fodor
and Pylyshyn (1988) dont explicitly appeal to
the conceptual constitution thesis.
They do not even appeal to the idea of conceptual
abilities.
But, as I noted above, that discussion invites
the interpretation that thought abilities are
constituted by conceptual abilities.

Suppose, however, that that is the intended
interpretationthat Fodor and Pylyshyn intend to
be asserting the conceptual constitution thesis.
Some points are worth noting.

First, the conceptual constitution thesis does
not imply the LOT thesis.
The claim that thought abilities are constituted
by conceptual abilities does not imply that there
is a language of thoughta mental symbol system
with a compositional semantics and types of
computational operations that molecular symbols
participate in in virtue of their syntactic and
other formal properties.
It does not, for instance, even imply that
concepts are mental symbols.

Second, connectionism faces a formidable
challenge indeed if it aims to explain, for
instance, why anyone able to think that John
loves Mary would be able to think that Mary loves
John, and vice versa, without invoking the
conceptual constitution thesis.

65
Constitution/Involvement

Third, the claim that a thought ability involves
conceptual abilities does not imply that the
thought ability is constituted, even in part, by
the conceptual abilities in question.

It would in no way be question begging for LOT
theorist to characterize systematicity laws as
laws concerning the co-possession of thought
abilities involving the same conceptual abilities.

Everyone should agree that a cognizer can
mentally represent that John loves Mary only if
the cognizer can mentally represent John.
That claim does not even imply that there are
mental representations, let alone that a mental
representation of John is a constituent of the
mental representation that John loves Mary.

Thus, it would not be question-begging for LOT
theorists to characterize systematically related
thought abilities as distinct thought abilities
that involve all the same conceptual abilities.

From my experience with the literature, I expect,
though, that some will reject the claim that the
ability to think that John loves Mary and the
ability to think that Mary loves John involve all
the same conceptual abilities.
I also expect that some will claim not to know
what thought abilities I am claiming involve all
the same conceptual abilities, beyond the
specific example that I have just cited.

The systematicity of thought can be
characterized, however, without assuming the
conceptual constitution thesis.
In fact, it can be characterized without replying
even on the assumption that there are conceptual
abilities.

I have labeled the laws that connectionism is
being challenge to explain systematicity laws.
What is at issue is what laws are systematicity
laws.

In partial answer to that question instances of
the schema that I stated earlier are.
Using the schema, I have identified a family of
systematicity laws without appeal to the
conceptual constitution thesis, the idea of
intrinsic connections among thought abilities, or
even the assumption that there conceptual
abilities.
In due course, I will identify further families
of systematicity laws by appeal to further
schemata, and will do so without appealing to any
of the matters in question.

Since I will employ schemata, I want first to
turn to a misguided would-be characterizations of
systematicity that has been offered in the
literature.
I will point out how it results from
misunderstandings of how schemata are used to
characterize systematicity, and, in some
instances, simply from misunderstandings of how
schemata are used.

74
Johnson (2004)

Kent Johnson (2004) tells us that although many
have claimed that thought and/or language are/is
systematic, there has been no adequate statement
of what systematicity is.
To remedy the situation, he offers a definition
of systematicity, and then argues that neither
natural language nor thought is systematic.

He correctly cites Matthews (1994) and Cummins
(1996) as maintaining that linguistic abilities
are systematic, while denying that thought is
systematic.
Let it suffice to note that the question for
anyone who accepts that linguistic abilities are
systematic yet denies that thought abilities are
systematic is this how can linguistic abilities
be systematic and the mental representational
abilities of language users fail to be?

In any case, Johnston focuses on the
systematicity of language, rather than the
systematicity of thought, because, he says, it
is easier to study overtly realized phenomena
like language (2004, p.112).
In fact, of course, in the linguists sense of
sentences as tree-structures (the sense in which
Johnson uses sentence), sentences are overtly
realized by sounds, marks on pages, or hand
movements only by virtue of how the sounds,
marks, or hand movements are causally related to
cognitive representations of language users.

Johnson makes it clear that it is not his concern
to defend the view that cognitive architecture is
connectionist, but only to remove the
systematicity challenge.
After making his case that neither language nor
thought is systematic, he says
Have I just vindicated connectionism?
Absolutely not. In fact, I have not altered the
evidential status of connectionism at all. I
have simply shown that whatever problems
connectionists models of language and cognition
may face, systematicity is not one of them.
(2004, p.137)

We should note that Johnson (2004) thinks that
language is productive.
He says There areinfinitely many words in the
typical speakers repertoire, because there are
recursive word-forming devices, for example,
great-grandmother, great-great-grandmother,
great-great-great-grandmother (2004, p.114).
Presumably, then, he thinks as well that at least
the systems of mental representation possessed by
language users are productive.

Johnson makes no mention of the productivity
challenge to connectionism.
Anyway, as should become clear later, any
productive system would be systematic in the
intended sense (it would be governed by
systematicity laws).

Johnson defines systematicity for a language as
follows
A language L is systematic if and only if (S)
holds for all A (S) A is a constituent of L only
if for all B of the same linguistic kind as A,
and all things C, C can compose with A (in a
certain way) to form a sentence if and only if C
can compose with B (in that same way) to form a
sentence. (2004, p.14)

Linguistic kinds are linguistic categories.
Johnsons definition is equivalent to the
following
a language is systematic if and only if the
members of its grammatical categories are
intersubstitutable salva congruitatethat is,
without loss of grammaticality.
Let us call this (S)-systematicity.

The languages of propositional logic and
first-order quantification theory are
(S)-systematic.
But not all artificial languages are
(S)-systematic.

For example, the classical computer language LISP
is not.
Thus, (CONS 'A 'B) is grammatical, but (CAR 'A
'B) is ungrammatical, even though CONS and CAR
fall under a common grammatical category.
A LISP sentence with CONS in the head is
grammatical if and only if the second term is an
atom and the third is either an atom or a list.
One cannot substitute CAR (or CDR, for that
matter) for CONS salva congruitate.

It is very well known that natural languages are
not (S)-systematic.
It is thus completely unsurprising that Johnson
says the only truly systematic systems of any
complexity that I know of are the languages of
logic and mathematics (p.132).

Johnson offers counterexamples for a number of
categories, including the categories of verb and
adjectives.
Here is an example of his for the category of
verb (2004, p.117)
(3) Alice showed Martha the book.
(4) Alice described Martha the book.

Examples for the category of verb, the category
of adjective, and for other categories abound.
As Johnson himself notes (2004, p.113), examples
of the sort that he gives can be found scattered
throughout the linguistics literature.

Here is an example from Fodor and Pylyshyn (1988,
p.29) concerning the category noun phrase that
suffices to show that English fails to be
(S)-systematic
(1) John and Mary are friends.
(2) John are friends.
Both John and Mary and John a members of the
category noun phrase.
But they are not intersubstitutable salva
congruitate.

Now given that Fodor and Pylyshyn (1988) use this
example and also claim that natural languages are
systematic, one wonders where Johnson got the
idea that systematicity should be defined by (S).
That is a matter I will return to shortly.

Of course, John and Mary is a plural noun
phrase, while John is not.
So, although they are both members of the
category noun phrase, the first is, but the
second is not a member of the category plural
noun phrase.

Although natural languages are not
(S)-systematic, it is the case is that if two
constituents are members of all and only the same
grammatical categories, then they are
intersubstitutable salva congruitate.
In other words, if two constituents A and B fail
to be intersubstitutable salva congruitate, then
one of the two is a member of a grammatical
category of which the other is not a member.
But that, notice, is true by definition of
grammatical category.

Johnston notes as much. He asks us to consider
the following definition
A language L is systematic if and only if (S)
holds for all A (S) A is a constituent of L
only if for all B of all the same linguistic
kinds as A, and all things C, C can compose with
A (in a certain way) form a sentence if C can
compose with B (in the same way) to form a
sentence. (2004, p.126)

He then says The problem with (S) is that it
is a tautology. The sum total of linguistic
kinds that a word belongs to exhausts its
grammatical properties by the very definition of
the linguistic kinds (2004, p.126).
It is certainly true that no one disputes that
natural languages are systematic in the sense of
(S).

On the other hand, it is, as I said, well known
that natural languages are not (S)-systematic.
The Fodor-Pylyshyn (1988) example suffices to
show that English isnt.

To return to the systematicity of thought, I know
of no reason whatsoever to think that the
language of thought is (S)-systematic but, to
the best of my knowledge, no proponent of the LOT
hypothesis has ever even suggested that it might
be, let alone claimed that it is.

Of course, if our system of mental representation
is a language, then (S) will hold for it.
But it would be dialectically utterly useless in
the context of the LOT/connectionism debate for
LOT theorists to appeal to (S) in posing the
systematicity challenge.
The reason isnt that it is a tautology that
languages are (S)-systematic.
The reason is that the question at issue is
whether our system of mental representation is a
language.

Of course, for the very same reason, it would be
dialectically useless to appeal to (S).
Only a language could be (S)-systematic.
How, then, could anything like (S) be relevant to
posing the systematicity challenge for thought?

This takes us back to the question I raised
earlier
Why Johnson does think that (S) is an appropriate
characterization of systematicity?

In defense of this characteriziation, he cites
(2004, p.113) the following proposal by Robert
Cummins
A system is said to exhibit systematicity if,
whenever it can process a sentence s, it can
process systematic variants of s, where
systematic variation is understood in terms of
permuting constituents or (more strongly)
substituting constituents of the same grammatical
category. (1996, p.594)
Johnson says of the very few explicit
characterizations of systematicity, Robert
Cummins offers one that gets really close to the
heart of the matter (2004, p.113).

Unfortunately, he doesnt tell us why he thinks
that it gets really close to the heart of the
matter.
In any case, Johnsons (S) is mainly intended to
capture this notion of Cummins.
Johnson shifts from sentence processing to the
grammaticality of a sentence, he tells us,
because we may well be able to understand (and so
process) ungrammatical sentences, and he takes
grammaticality, rather than sentence
understanding to be the heart of the matter
(2004, p.113).

100

But Cumminss notion of a systems exhibiting
systematicity is not invoked by any LOT theorists
in the characterization of systematicity.
It is Cumminss own idea and presented by him as
such.

101

Any formulation of systematicity along these
lines would be utterly useless to LOT theorists
since the point of appealing to linguistic
systematicity is to make a case that sentences
have constituent structures, and the
characterization of systematicity in question
implies that they do.

102

Anyway, the main point to note is that Johnston
gets the idea for (S)-systematicity specificially
from Cumminss remark or (more strongly)
substituting constituents of the same grammatical
category (1996, p.594).
Johnson picks up this ball dropped by Cummins and
then runs with it.

103

It is worth mentioning that I think that Johnson
reads Cummins uncharitably.
A charitable reading would have plugged in the
words in any way that preserves grammaticality
at the end of the remark.
One would think that that would capture Cumminss
intention.

104
Evans Generality Constraint

Johnson also cites as inspiration for (S), Gareth
Evanss formulation of the Generality Constraint
on thoughts, which is intimately related to the
hypothesis that thought is systematic (see Davis
1991).
It is a spelling out of what I called the
conceptual constitution thesis.

105
Evans Quotes

Johnston cites the following passages from Evans
(1982)
It seems to me that there must be a sense in
which thoughts are structured. The thought that
John is happy has something in common with the
thought that Harry is happy, and the thought that
John is happy has something in common with the
thought that John is sad (p.100).
The Generality constraint requires us to see the
thought that a is F as lying at the intersection
of two series of thoughts the thoughts that a is
F, that a is G, that a is H,, on the one hand,
and the thoughts that a is F, that b is F, that c
is F,., on the other (p.209 cf. p.104, fn.21).

106

Johnson says
although Evans is primarily concerned with
thought, he illustrates the Generality Constraint
with language (1982, pp.101-03). Others have
discussed it in a linguistic context. Thus, (S)
captures a property that is often believed to
hold of language. (2004, p.115)

107

Johnson says that Evans illustrates the
Generality Constraint with language, I take it,
because Evans illustrates the sort of thing he
has in mind by claiming that the ability to have
the thought that Harry is happy is a complex
ability by analogy to the sort of thing we have
in mind when we say that the understanding of a
sentence such as Harry is happy is a complex
ability.

108

As I noted, though, rather than it being often
believed that (S) holds of natural languages, it
is very well known that (S) fails for natural
languages.
As I also noted, the sorts of counterexamples
Johnson gives to the claim that English is
(S)-systematic are rife in the linguistic
literature, as he himself acknowledges.

109

Presumably, then, Johnson means just that it is
often believed by philosophers of mind and
language, or something of that sort.
In my experience, however, that is not true.
And could Johnson have actually thought that
Fodor and Pylyshyn think languages are
(S)-systematic?
As we saw, their paper includes a counterexample
to that claim.

110

Moreover, so far as I know, no contemporary
philosopher has maintained that (S) holds for our
system of mental representation.
It is puzzling why Johnson thought that the
passages from Evans indicated that Evans was
presupposing that (S) is true of natural
languages or of thought.

111

The following remarks by Johnson, which appear in
a footnote twenty one pages after he states (S),
gives a clue

112

Some philosophers (for example, Evans in the
quote at the beginning of this article) have
simply assumed that the structure of thought has
no interesting or restrictive structure. They
assume, for example, that the structure of Mary
loves John has simply the form of a two-place
relation LmjBut adopting such a position
requires making some extremely strong empirical
assumptions about the structure of thought. I am
unaware of any empirical evidence that supports
these assumptions. (2004, p.135)
The Evans quote Johnson mentions in the
parenthetical remark in first sentence above is
the one we cited above from Evans.

113

It is, I believe, deeply uncharitable of Johnson
to read Evans as claiming that thoughts are
structured like sentences of first-order logic
(what I have been calling predicate logic).

114

Evans, I believe, uses the first-order logic
schemata in question simply as a way of
indicating the sorts of generalizations about
thought that he thinks make the case that
thoughts have structures, in the sense that
thought abilities are constituted by conceptual
abilities.
The philosophical literature is rife with uses of
sentence schemata to indicate relevant
generalizations, without that being made
explicit.

115

Evans is not claiming, nor is he presupposing,
that the structures of mental representations are
or are very much like (Johnston (2004, p.135))
those of sentences in the formal language of
first-order logic.
Indeed Evans is not even presupposing that there
is a language of thought, let alone one with that
has a grammar like the grammar of first-order
logic.

116

In the passage from Johnson quoted above,
Johnston may be using Mary loves John to name a
mental representation.
It is hard to tell since italicization is the
device he uses in the paper to name English
sentences.
But, in any case, his discussion suggest that he
thinks that to take the English sentence Mary
loves John to be an instance of the schema Lmj
is to take it as having simply the form (2004,
p.135) of Lmj.

117

If he does not think that, then it becomes all
the more puzzling why he thinks taking the mental
representation Mary loves John as an instance of
the schema requires taking it to simply have the
form of Lmj.
If taking natural language sentences to be
instances of the schema does not require taking
them to have the form Lmj, why would taking
mental representations to be instances of the
schema (something I think Evans does not do)
require taking them to simply have the form
Lmj?

118

It is, however, is a simple misunderstanding of
what it is for a sentence to be an instance of a
predicate logic schema to think that taking Mary
loves John to be an instance of Lmj requires
taking the sentence to simply have the form of
Lmj.

119

If for a sentence to be an instance of a
predicate logic schema, the schema had to
represent all or virtually all or even much of
the structure of the sentence, predicate logic
schemata would have no instances in natural
languages.
It is controversial exactly how predicate logic
schemata and the natural language sentencesthe
tree structuresthat are their instances of them
are related.
But everyone thinks that such schemata leave a
lot of structure unrepresented.

120

Johnson gives us no reason to doubt that
predicate logic schemata have instances in
natural language.

121

Moreover, for our present purposes, we could, if
we liked, avoid appeal to predicate logic
schemata like aRb yet still identify vast
families of systematicity laws using schemata.

122

As Johnson reminds us, we still dont have the
final theory of the grammar of English.
It is, however, to put it mildly, hardly
contentious to claim that we know enough about
the English sentences Mary loves John and John
loves Mary, for instance, to know that they lack
any truth-functional structure.
Given that, they are instances of the ps and
qs of propositional logic.

123

Here is a schema whose application to a natural
language sentence requires only the assumption
that the antecedents and consequents of the
conditionals contained in them lack any truth
functional structure
A cognizer is able mentally represent that if p
then q if and only if the cognizer is able to
mentally represent that if q then p.
Instances of this schema too are systematicity
laws.

124

Before concluding the discussion of Johnsons
paper, we should note that given what it is (by
stipulation) for something to be an instance of a
sentence schema, only grammatical sentences can
be instances of sentence schemata.

125

Under appropriate stipulations for a, R, and
b, the sentence John bakes bread is an
instance of the predicate logic schema aRb.
But even under those stipulations, the
ungrammatical string of words Bread bakes John
is not.
Indeed Bread bakes John is not an instance of
any predicate logic schema.

126

Thus, it would be simply a mistake to think, for
instance, that the string of words
Ceteris paribus, a cognizer is able to mentally
represent that John bakes bread if and only if
the cognizer is able to mentally represent that
bread bakes John
is an instance of the schema
Ceteris paribus, a cognizer is able to mentally
represent that aRb if and only if the cognizer is
able to mentally represent that bRa.
It is not and so the ungrammatical string of
words in question is irrelevant to the issue of
whether all instances of the schema are true.

127

I suspect that no single sentence schema could be
formulated that is such that it could be claimed
that all systematicity laws are instances of it,
at least without raising issues about the
structures of natural language sentences that are
controversial in the context of the
LOT/connectionism debate.

128

But we can make do with less by doing with more.

129

Unlike the grammar of English or any other
natural language, the grammar of predicate logic
(which includes the grammar of propositional
logic) is completely understood.
If we avoid using the horseshoe (using instead
the English ifthen), we can appeal to
predicate logic schemata to identify families of
systematic laws without making any particularly
controversial assumptions about the structures of
natural language sentences.

130

Moreover, it should be noted that using such
schemata in this way by no means presupposes that
the rules of inference of predicate logic are
among the correct rules of inferences.
The reason is that no use whatsoever is made of
those rules of inference.
We rely only on the grammar, on what counts as a
well-formed formula, not on any of the rules of
inference.

131

I have already so employed two such predicate
logic sentence schemata, which, when fully and
properly ticketed, are
(SG1) Ceteris paribus, a cognizer is able to
mentally represent that aRb if and only if the
cognizer is able mentally represent that bRa.
(SG2) Ceteris paribus, a cognizer is able
mentally represent that if p then q if and only
if the cognizer is able to mentally represent
that if q then p.

132

Instances of these schemata are systematicity
laws.
They are among the psychological laws that must
be explained to meet the systematicity challenge.

133
Some Further Schemata

(SG3) Ceteris paribus, a cognizer is able to
mentally represent that if (P and Q) then R if
and only if the cognizer is able to mentally
represent that if P then (Q and R).
(SG4) Cetreris paribus, a cognizer is able to
mentally represent that P and not-Q if and only
if the cognizer is able to mentally represent
that not-P and Q.
(SG5) Ceteris paribus, a cognizer is able to
mentally represent that ((P and Q) or R) if and
only if the cognizer is able to mentally
represent that (P and (Q or R)).

134

LOT theory offers a unified account of the laws
that are instances of (SG1)-(SG5) as well as the
vast numbers (an unbounded number if language is
productive) of other systematicity laws.

135

Anyone familiar with the grammar of predicate
logic could, with a little thought, expand the
above list to identify some further families of
systematicity laws.
Hint In thinking about how to expand the list,
one can of course rely on ones intuitions about
what sorts of thought abilities involve the same
conceptual abilities if (like me) one has such
intuitions.

136

But if connectionists claim not see how to expand
the list and that they remain in the dark about
what laws are systematicity laws, no matter.
Each of the above schemata suffices to identify a
truly vast body of psychological laws that
connectionism must explain, and explain without
implementing a LOT architecture, in order to meet
the systematicity challenge.

137

Connectionists can begin to try to meet the
systematicity challenge by explaining the laws
identified by (SG1)-(SG5) without implementing a
LOT architecture.

Write a Comment

User Comments (0)