TO APPEAR IN:
Language down the garden path: The cognitive and biological basis for
linguistic structure
Montserrat Sanz, Itziar Laka, Michael Tanenhaus (Eds.)
Chapter 14
On abstraction and language universals
Massimo Piattelli-Palmarini
14.1 Introduction
Tom Bever and I, over the years, have been discussing many problems and issues in
linguistic theory and its surroundings. One of them keeps regularly coming up and I think
I owe him a more reflexive explanation of the way I see it. He would formulate it as
follows: are the basic internal structures of language and bona fide linguistic universals
caused or uncaused? Another, more traditional, phrasing is: should the theoretical linguist
adopt a Platonist conception of her object of inquiry? Is the job of the theoretical linguist
more akin to that of the mathematician, or rather to that of the natural scientist, say the
physicist or the biologist? Mathematicians and logicians assume, explicitly or otherwise,
that they are discovering properties, relations and necessary truths about abstract objects.
Discover is a performative verb and it presupposes the existence of its object. The late
Gorge Boolos, a giant in the field of mathematical logic, once told me: ‘The alternative
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has never been adequately proposed’. The alternative, that is, to a Platonist conception of
his whole field of inquiry.
Linguists like Paul Postal, Terence Langendoen, the late Jerrold Katz and Tom
Bever himself have espoused a Platonist stance, while Chomsky has always been
adamant in taking the naturalist’s point of view. Even in the present Minimalist Program,
where the pursuit of virtual conceptual necessity in all the entities that are being
postulated is relentless, Chomsky states in no ambiguous terms that no Platonism is
introduced and no ‘E-linguistic’ notions: ‘only biological entities and their properties’
(Chomsky, N. 2001) p.42). In the concluding section of this important paper, Chomsky
examines the ontological (non)status of ‘derivations’, that is, the actual computations of
Narrow Syntax, and of the expressions produced by the language faculty. Steering a way
that avoids both Platonism and sheer externalism (the E-language approach, where
language is conceived as an objective, external, public, socially generated set of
expressions), Chomsky says: ‘these are not entities with some ontological status; they are
introduced to simplify talk about properties of the language faculty FL and [of its internal
states] L, and they can be eliminated in favor of internalist notions’. Then, allegedly
scoring what Paul Postal has labeled ‘the most irresponsible passage written by a
professional linguist in the entire history of linguistics’ (Postal 2004: 296). (Postal, P.M.
2004)(For a refutation see (Collins, J. 2009)), Chomsky underlines the relation between
mathematics and linguistics: ‘One of the properties of Peano’s axioms PA is that PA
generates the proof P of ‘2 + 2 = 4’ but not the proof P’ of ‘2 + 2 = 7’ (in suitable
notation). We can speak freely of the property ‘generable by PA’, holding of P but not P’,
and derivatively of lines of generable proofs (theorems) and the set of theorems without
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postulating any entities beyond PA and its properties. (Chomsky 2001: p.41, my
emphasis). He then adds: ‘Similarly, we may speak of the property ‘generable by L’,
which holds of certain derivations D and not others, and holding derivatively of an
expression Exp formed by D and of the set {Exp} of those expressions. No new entities
are postulated in these usages beyond the faculty of language FL, its states L and their
properties. Similarly a study of the solar system could introduce the notion HT =
{possible trajectories of Halley’s comet within the solar system}, and studies of the
motor organization or visual perception could introduce the notions {plans for moving
the arm} or {visual images for cats (vs. bees)}. But these studies do not postulate weird
entities apart from planets, comets, neurons, cats, and the like.’ (Again, my emphasis).
Some years ago, Chomsky, in private conversation, confessed to me that he regretted the
title he had given to an influential book of his (please notice: he regretted only the title):
Knowledge of Language (Chomsky, N. 1986)) because it suggests the idea that there is
this object, language, of which we have knowledge. The central notion, the only entity
having an ontological status, is, instead, this internal apparatus, the Faculty of Language,
and its internal computational states L. Its episodic, fleeting and variable output, the set
of expressions {Exp}, devoid of any ontological status, is what is commonly and prescientifically called language (more precisely, in his approach, E-language).
It needs to be stressed that a Platonist conception is also, though in a quite
different way, an externalist one. Rather than ‘knowledge of’, it postulates ‘access to’
abstract entities and relations that are outside the mind. They are there, regardless of
human mental activities. The task of the child and of the adult speaker is to discover them.
The task of the theoretical linguist is to unveil how this discovery is possible. In a sense,
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it’s like a vision scientist trying to determine how the visual system of a certain species
has access to relevant and less relevant aspects of a visual scene. However, in this case,
the ‘scene’ is composed of abstract entities and their relations and the eye is the mind’s
eye. Unlike in the case of vision, postulating the independent existence of such entities is
what constitutes the controversial Platonist stance.
Before I come back to language, I will make a brief digression into another
domain that has attracted my attention for several years: judgment and decision making
(Piattelli-Palmarini, M. 1994). I admit to being tempted by a Platonist conception in this
field. The reason why we think we have ample evidence of cognitive illusions
(probabilistic illusions, neglect of base rates, overconfidence, ease of representation and
the like) is that we know what the correct rational responses and the right intuitions
would be for the problems presented. These are ‘right’, ‘correct’ and ‘rational’ because
proofs are available. We can say confidently that the untutored mind systematically ‘falls’
for a certain kind of cognitive illusion and describe how that illusion works because we
know what it would be not to fall for it. A proof based on, say, normative probability
theory or set theory or formal logic is a reliable basis to draw such conclusions. The
reason why a proof is valid (or isn’t) is not to be found in psychology, it’s to be found in
the properties of abstract entities. Upon suitable training (a whole course on logic, set
theory, probability theory, etc.) we come to accept, we get access to, these necessary
truths. These are not truths because we end up believing them. Rather, we end up
believing them because they are truths. Causality goes in this direction and the status of
necessary truths is itself (to use Tom’s illuminating term) uncaused. We have reasons to
think that it is what it is regardless of human mental processing, that it would be what it is
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even if no human mind ever existed. If this is Platonism, so be it. Like Boolos, I do not
see any viable alternative.
Now, about language. The situation there, it seems to me, is different. I need one
concrete example to bring the point home: The conservativity of determiners.
14.2 The conservativity of determiners
There is a vast literature on this (Higginbotham, J. 1994; Higginbotham, J. 1995;
Higginbotham, J. and R. May 1981; Higginbotham, J.T. 1991; Keenan, E.L. and J. Stavi
1986; Ludlow, P. 1995; Pietroski, P. 2002; Uriagereka, J. 1996; Uriagereka, J. 1998) and
I have tried my hand on this topic too (Piattelli-Palmarini, M. 2008). Putting this in as
simple a way as I can think of, in the present context, let’s consider a generic relation
between two sets {A} and {B}. Assuming that their intersection AB is not empty, we
can consider a rather curious condition (called intersectivity or conservativity):
(1)
AB = (AB)  A
In words: the overlap between A and B is exactly the same as the overlap between
their overlap and the set A itself.
This is a quite restrictive and somewhat peculiar restriction. A model with only
two individuals, and 4 properties, that is, a combinatorial with 24= 16 possibilities, gives
65,636 possible functions from one set to another. Probably (Keenan and Stavi 1986)
only 512 of these are conservative, that is less than 8 in one thousand. It’s easy to find
relations that are asymmetric and transitive, but not conservative. Take the asymmetric
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relation ‘trump’ in the game of poker. Four of a Kind (say, four aces and one king)
trumps a Full House) (three aces and two kings), and Full House trumps Three of a Kind
(three aces, one king and any other card), but the intersection of Four of a Kind and a Full
house gives three aces and one king, now we have a tie, and this is not the same relation
as the one we started with. So, we have asymmetry and transitivity, but not conservativity.
Let’s now turn to the determiners of natural languages. Ever since William of
Sherwood, it has been remarked that the two following sentences have identical
truthmakers:
(2)
a. All men are mortal.
b. All men are mortal men.
These two sentences are truth-valuationally exactly the same. Let’s indicate this
equivalence with .
(3)
No ecologist is a hunter  No ecologist is a hunter who is an ecologist.
This does not apply only to quantifiers, but to all determiners.
(4)
a. The Tuscans are Italians.  The Tuscans are Tuscan Italians.
b. A building was designed by Frank Gehry  A building was a Frank-Gehrydesigned building.
All determiners of all human natural languages are conservative. It’s easy to
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invent impossible determiners that are non-conservative. Let’s bring in mind that the
order of the arguments of a determiner is crucial. Conservativity is an ordered relation
between sets. Determiners are two-place predicates: One is the ‘restriction’ (mortal,
hunter, Tuscans, designed by Frank Gehry) (the internal argument), the other is the
‘scope’ (men, ecologists, Italians, buildings) (the external argument). The truth
conditions for All men are mortal are quite different from those of All mortals are men
(which is obviously false). Let’s now consider the imaginary determiner *gre (due to
Paul Pietroski). Let’s compare the ordinary the with *gre.
(5)
a. The bottle fell  The bottle is the-object-that-fell-bottle
b. *Gre bottle fell  *Gre object-that-fell is the bottle-that-fell.
Suppose a cup fell, but no bottle did. We have different truth-makers for the two
expressions. Therefore *gre would not be conservative.
Even simpler is the imaginary quantifier *trall (due to Juan Uriagereka). Compare
*trall with the ordinary all.
(6)
a. All sharks eat fish  All sharks are fish-eating sharks.
b. *Trall sharks eat fish  All fish are eaten-by-shark fish.
Notice that none of these impossible equivalences is ‘hard for thought’, nor would
such non-conservative quantifiers impede communication. The impossible determiners
are impossible because they would invert the restriction and the scope. As pointed out by
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Mark Baker and Richard Larson, in different ways and in different contexts, an
impossible determiner would be analogous to an impossible transitive verb that swaps
internal and external argument. Say, the impossible verb *trexasperate such that the
active form children often *trexasperate their parents would mean that parents are often
exasperated by their children. A banal thought not expressible in that straightforward
active form by way of such imaginary verb. The impact of the conservativity of
determiners on syntax overall is remarkable. Determinants, being conservative, are closed
under Boolean operations (negation, disjunction, conjunction, conditionalisation) not
every, most but not all, the….or a….. They preserve monotonicity (downward
entailingness in one of their argument and upward entailingess in the other, or in both, or
the reverse). They generate the right syntax for polarity items
(7)
a. Whatever cups are in the cupboard, they are covered with a cloth.
b. *Whatever cups are in the cupboard, they are covered with any cloth.
c. No liberal and at most six conservative delegates attended any meetings this
year.
d. *All liberal and all conservative delegates attended any meetings this year.
They allow correct Case-checking (Larson and Yamakido 2005, 2006). In fact,
[+N] complements of determiners, obviously, bear a Case feature that must be checked.
Det checks one Case on its internal argument (its restriction), just as transitive verbs
check one Case (Accusative) on their internal argument. Case checking on their external
argument (scope) bears strong and interesting similarities with raising.
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DP-modifiers that do not bear Case features (essentially PPs and CPs) can remain
in situ, while those that do (APs) must move to a site where Case is checked (unless some
other means is made available). There are interesting parametric differences between
languages
(8)
a. Every woman with courage (PP)
b. *Every woman courageous (AP)
c. Every woman who was invited (CP)
d. *Every woman invited
Italian:
(9)
a. Ogni donna coraggiosa (OK)
b. Ogni donna invitata (OK)
The conservativity of determiners is genuinely a universal, because no exception
has been found so far. Moreover, conservativity has been ascertained in all Indoeuropean
languages, including a language with postpositional DP-cliticization (Basque), Western
Indo-Iranian (Farsi, Kurdish, Zazaki, Hawrami) (Larson and Yamakido, 2005, 2007), the
languages spoken by the most remote and isolated communities in the Kalahari Desert
(Khoisan) (Huybregts 2002), any one of the click languages and a creole language
'assembled’ only very recently (Haitian) (Déprez, 1999, 2005).
The explanation of the conservativity of determiners, a rather peculiar kind of
language universal, cannot be pragmatic, nor communicational, nor based on some
general limitation on cognition. It’s not, either, a reflection (whatever that could mean) of
the mind’s spontaneous innate access to set-theoretic properties and functions between
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sets, because (as we mentioned) conservativity is exceedingly rare in that abstract domain.
It rather appears to be explicable by an interaction between syntactico-semantic structures
and computations thereof. Cutting a long story very short, what seems to be involved is:

The asymmetry between Det restriction and Det scope (as we saw)

Deep similarities between verbs and determiners, involving an ordered alignment
of scope and restriction (akin to Mark Baker’s UTAH)

Case-checking being as local as possible

Constituency (a DP must be a constituent)

DPs having several (all?) properties of phases

Parametric differences between languages in the combination of determiners and
adjectivals and participials (*all women old and *many jewels stolen are
impossible in English, but perfect in other languages (say, in Italian, Spanish
and French)

The uniformity of raising (Hornstein and Uriagereka)

Chain-formation and re-merging
These factors are all to be considered under the usual application of strict semantic
compositionality. I have selected conservativity because it is a very abstract language
universal but it cannot be explained by standard logical predicate-argument relations,
elementary logical quantification or some generic ‘laws of thought’. It cannot be
explained either by external factors, nor by language processing constraints. So, what is it
status?
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14.3 The status of this universal
Chomsky’s reflections on mathematics versus linguistics, far from being as ‘irresponsible’
as Postal claims, also apply to this case.i A language universal supports counterfactuals.
With enough ingenuity and time, one can spin off countless examples of impossible
expressions, constituting violations of a linguistic universal; in our case, impossible
form/meaning mappings and impossible equivalences. The kinds of non-conservative
determiners that have been invented and offered in this rich literature (and of which we
have seen two examples above) are never found in any language. We can suppose that
no child could learn them, in spite of the banality of the associated meanings, just as she
could not learn a verb like trexasperate. Constraints on internal computations in the
domain of language explain both this universal and these impossibilities. Although the
details still escape us, it’s safe to assume that the conservativity of determiners is caused
by such constraints.
Let’s now consider a related issue. What appears to be uncaused is the paucity of
the fraction of conservative relations in the domain of all functions between two sets.
Keenan and Stavi’s theorem is a theorem. They discovered this relevant truth. Had it not
been so, had the fraction been huge, this universal would have been a lot less intriguing.
It would have been like the linguistic universal that, in first and good approximation,
predication expresses set intersection (a brown cow is something that belongs both to the
set of cows and to the set of brown objectsii) and that conjunction expresses set union (the
set of ‘children and adolescents’ is the union of these respective sets). The operations of
set intersection and of set union and the resulting properties of the sets involved are
abstract entities and a Platonist can conjecture that the human mind is so structured that it
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has access to them. In the case of conservativity, however, it would be problematic to
conjecture that the human mind in the domain of language has access to the abstract,
mind-independent properties of functions between sets, ascertains (tacitly of course) that
only a tiny fraction of these possesses the property of conservativity and somehow
decides that a pivotal component of the closed-class lexicon, i.e., the determiners, will
conform to it. My inclination is rather to conjecture that the computationally constrained
language faculty, in this domain, generates a specific kind of expressions, the output of
an ordered relation between two sets. As a consequence, this relation has a certain
property: the property of conservativity. When suitably analyzed in the general context of
all such functions, it turns out that the corresponding set is quite small. Why this is the
case and what kind of truth this is, lies outside the domain of linguistics. The issue can be
safely left to the mathematicians. What is relevant to linguistic inquiry is that
notwithstanding the utter marginality of this class of functions, conservativity is a
universal property of a core linguistic component (the determiners). The ontological
status of this marginality should not be confused with the ontological status of its
consequences for linguistics. Just like the ontological status of the forces that determine
the tides must not be confused with that of the consequences that tides have on the life of
sailors.
What we have just seen is a deep, abstract linguistic universal that can be
plausibly attributed to properties of the output of the internal (syntactico-semantic)
machinery.
14.4 On abstraction
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In Piaget, abstraction is a central cognitive ‘engine’, acquired progressively, in a stepwise
fashion, reflecting the ‘necessity’ of mathematical constructions. He was no Platonist,
though. The ascending ‘stages’ of abstraction were, in his theory, the logically necessary
unfolding of abstract structures, in fact the result of operations (thematization,
reversibility, reflective abstraction and so on). The formal results of these classes of
operations were, in his opinion, ‘justified’ (sic) by these mathematical constructions. It is
not that the child has ‘access’ to these formal relations because they are somewhere in an
empyrean world up there, outside us, but rather because the child’s mental operations, in
sequence, inevitably reproduce all and only the structures that those operations are bound
to obtain, because of the very nature of abstract entities. Since I have never been
convinced by the Piagetian system, I will not try to make this coherent. Suffice it to say
that the nature and role of abstraction was quite different in Piaget than it is in Chomsky.
In Chomsky abstraction is primitive, instantaneous, natural to the system, automatic. The
class of the very few (in the limit one only) admissible generalizations from poor stimuli
is constrained by our nature. It’s domain-specific, not general. It’s justified (not a concept
that is germane to him) by the simplicity, elegance and predictive power of the
hypotheses. Just as in physics, chemistry, biology, no other ‘justification’ is needed, or
possible. The relentless search for such abstractions has propelled the theory ever after.
The central requirement of ‘explanatory adequacy’ commits the linguist to innately
attribute to the child the best (simplest, most compact, most elegant) hypothesis that the
linguist has discovered. It’s a naturalized notion of abstraction.
14.5 A kind of conclusion
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I think that there are no necessary truths in the field of linguistics, just as there are no
necessary truths in other domains of natural science. Unlike in logic and mathematics, the
truths we discover (when we are lucky enough to do so) are never ‘necessary’, but rather
the fallible outcome of a rational integration between empirical data and our science
forming faculty. Simplicity, compactness, inferential power and range of coverage are
properties that our mind privileges, because we are what we are cognitively, as a species.
This is a quite elusive process that philosophers of science have been trying to elucidate
for a long time. Even in the present Minimalist Framework, the principles are virtually
conceptually necessary (emphasis on the qualification ‘virtual’), and, as a consequence,
more similar to physical principles than to biological ones. I will adopt a Chomskyan
strategy: if there is an issue of Platonism in linguistics, then it’s just like the Platonist
issue one (possibly) has in physics. If physicists are not troubled by it (and I don’t think
they are), then we should not be troubled either. Not that I hope to have persuaded Tom.
Simply, I tried to make it a bit more clear what my position is. Without his incessant and
blessed challenge on this topic, I would not have developed these reflections. I thank him
and await his further challenge.
References
Chomsky, N. (1986). Knowledge of Language: Its Nature, Origin, and Use. New York,
Praeger Scientific.
Chomsky, N. (2001). Derivation by phase. Ken Hale: A Life in Language. Kenstowicz,
M., (Ed.).Cambridge, MA, The M.I.T. Press: 1-52.
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Collins, J. (2009). ‘A Question of Irresponsibility: Postal, Chomsky, and Gödel.’
Biolinguistics 3(1): 099-103.
Higginbotham, J. (1994). ‘Mass and count quantifiers (reprinted in Bach et al. 1995).’
Linguistics and Philosophy 17(5): 447-480.
Higginbotham, J. (1995). Mass and count quantifiers. Quantification in Natural
Languages. Bach, E., E. Jelinek, A. Kratzer and B. H. Partee, (Eds).Dordrecht,
Holland, Kluwer: 383-419.
Higginbotham, J. and R. May (1981). ‘Questions, quantifiers and crossing.’ The
Linguistic Review I: 41-80.
Higginbotham, J. T. (1991). ‘Remarks on the metaphysics of linguistics.’ Ling. Phil. in
press.
Keenan, E. L. and J. Stavi (1986). ‘A semantic characterization of natural language
determiners.’ Linguistics and Philosophy 9: 253-326.
Ludlow, P. (1995). ‘The logical form of determiners.’ Journal of Philosophical Logic
24(1): 47-69.
Piattelli-Palmarini, M. (1994). Inevitable Illusions: How Mistakes of Reason Rule our
Mind. New York, Wiley.
Piattelli-Palmarini, M. (2008). Events and Conservativity: Clues towards Language
Evolution. Knowledge, Language, and Interpretation. On the Philosophy of
Donald Davidson,. Amoretti, M. C. and N. Vassallo, (Eds).Frankfurt, Ontos
Verlag/Transaction Books: 81-105.
Pietroski, P. (2002). Monadic determiners: Quantification and thematic separation.
University of Maryland.
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Postal, P. M. (2004). Skeptical Linguistic Essays. Oxford UK, Oxford University Press.
Uriagereka, J. (1996). Warps: Some thoughts on categorization. Cuadernos de Linguistica
IV. Ausin, A. and E. Lopez, (Eds).Madrid, Instituto Universitario Ortega y Gasset.
Uriagereka, J. (1998). Rhyme and Reason: An Introduction to Minimalist Syntax.
Cambridge, MA, The MIT Press.
i
I am leaving out the issue of finitary versus infinitary metamathematics, so central in the
Postal/Collins exchange, and the ontological status of infinite sets. I fail to see any
problem in positing that the orbit of a planet is an infinite set of points, or that a speaker
who would live a life without end would produce an infinity of well-formed sentences of
her language. These idealizations do not commit one to a Platonist metaphysics, nor are
they incompatible with it.
ii
Well, strictly speaking, ‘brown for a cow’, but let’s leave out this kind of issues here.
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