Hierarchy, Merge, and Truth San Sebastian, June 2006

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Hierarchy, Merge, and TruthSan Sebastian, June
2006

• Wolfram Hinzen
• Universiteit van Amsterdam, University of Durham

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The deflowering of trees

• Traditional assumption that linguistic expression
  are hierarchically structured objects.
• XP
• XP the
• XP the book the book
• Whatever hierarchies exist needs explanation in
  line with the SMT.
• Does minimalist syntax exhibit phrase structural
  hierarchies? (Chametzky, 2000, 2003 Collins,
  2002)

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Hierarchy via labels? Hornstein (2005)

• Merge is concatenation
• Concat (A,B) def A?B, with A, B atoms
• A non-hierarchical system
• Concat (C, A?B) C?A?B
• Enter labels, the crucial evolutionary
  innovation
• Concat (C, A?B) C?A A?B, with C, A A?B
  atoms
• Labeling identifies a complex structure with one
  of its (atomic) inputs.
• But why should the system be hierarchical?
• Labels are both unnecessary and insufficient to
  yield it.

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Labels are lexical items

• Chomsky (2001, 2005) Labels are the only probes
  and goals, the only thing the syntax ever sees
  only the interfaces ever see phrases.
• Due to the recursiveness of Merge, labels must be
  lexical items.
• Collins (2002) three explanatory factors for
  syntax
• (i) interaction of the properties of lexical
  items
• (ii) economy conditions
• (iii) interface (bare output) conditions.

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Deflating hierarchyThe Minimal Language
experiment

• Hierarchy ...is automatic for recursive
  operations, conventionally suppressed for those
  that merely enumerate a sequence of objects
  (Chomsky, 2005).
• Merge is recursive set-formation, n-ary abstract
  from substantive lexical content (meaning), and
  assume LEX?. Then
• ? 1
• Merge (1) ? 2
• Merge (2) ? 3
• Merge (3) ? 4
• Etc.
• Merge applied in this manner yields the
  successor function.

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Deflating hierarchy (cont.)

• c0 ? and cn1 cn, for all n.
• Suc(X) def X ? X
• X ? 1
• Succ(1) ?12
• Succ(2) ?, ?1, 23
• Succ(3) ?, ?, ?, ? 1, 2, 3 4
• Etc.
• It is straightforward to define addition in
  terms of Merge (X,Y), and in familiar ways, the
  rest of arithmetic. (Chomsky, 2005)

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Emergence of an ontology

• Ontology emerges by imposing structure on an
  unstructured set (space), which results in new
  spaces, which form a hierarchy, and each of which
  has specific topological and algebraic
  properties.
• (N,) is a half-group
• (N,,0) is a monoid
• groups are monoids with inverses for each element
• e.g., (Z,) is an (Abelian) group, arising out of
  N through making inverses with respect to
  defined.
• (Q,) is also a group, arising from Z by adding
  inverses w.r.t. multiplication.
• R arises from Q through topological completion
• With two inner operations, we get a ring, and
  with an inner and an outer operation, a vector
  space.

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Ontology in multiple dimensions

• Dimension of the vector space that Succ generates
  is 1.
• Intuitive concept of multiple dimensions a
  series of series of series (Russell 1903)
• Most general concept of a dimension in
  mathematics chain length. E.g.,
• length of sub-spaces of a vectorspace contained
  in one another
• length of prime-ideals in a ring
• chain of manifolds included in one another (a
  form of recursion)
• In MP and evolution, number and multiply
  dimensional spaces should simply come for free.
• Dubischar et al. 1999 One of the main ideas of
  this paper is to use geometrical structures, not
  on the Euclidean space (in which the brain is
  located), but on the cognitive information space
  X (space of ideas).

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Ontological categories in the parts of speech

• Abstract objects
• Objects with a substance/mass
• Objects with a form/boundary
• Objects with change potential
• States
• Activities
• Accomplishments
• Achievements

Entail- ment
Entail- ment
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Correlations

• Syntax Semantics
• NP/DP objects/reference
• CP truth/judgements
• TP tensed events
• vP events
• (bare) SCs predication
• internalism
• externalism

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Where does the lexical ontology come from?

• EITHER it might be extra-linguistic i.e., all of
  this is thought, or semantics.
• But it seems circular to blame much of this
  structure on the nature of the external physical
  world.
• OR it might be a reflection of structural
  complexity in the concepts denoting the
  respective objects.
• But there may not be any such structure internal
  to lexical items at all (atomism, Fodor 1998)
• However, there are systematic interrelations
  between these atoms (in particular, the necessary
  entailments), which moreover seem to be
  structure-driven.

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An internalist proposal HinzenUriagereka, 2006

• There is a syntactic structure to these things,
  but it is not accompanied by a compositional
  semantics.
• This yields entailments if the syntactic
  structuring is such that a hierarchy is built
  into the architecture of the formal system
  itself, i.e. the system is multi-dimensional.
• Essential intuition (taken from Uriagereka,
  1995) LEX provides unstructured conceptual
  spaces (atoms) through a small-clause adjoined
  predicate this space is structured, giving it a
  particular presentation.

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Constructing a complex concept the fabric of
reference
Nothing is on top here.

• Animate SC
• Count Presentation SC
• Mass Presentation SC
• Abstract Presentation Space PREDICATE
  SUBJECT

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Back to structure-building (Merge) as modeled on
Succ

• Merge qua set-of is n-ary a form of hierarchy
  follows automatically when n2.
• Merge(1,2)1, 2
• Merge(3, 1,2)3, 1, 2
• Etc.
• kill, buffalo
• Hill, kill, buffalo
• -ed, Hill, kill, buffalo
• Merge thus construed yields a mono-categorial and
  in this sense non-hierarchical system it never
  produces anything ontologically new (labels dont
  help in this regard).

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Adjuncts

• Pure adjuncts exhibit a (particularly simple)
  form of dependency
• walk quickly
• ?e walking (e) quick (e)
• Characterized mainly negatively
• a. Adjunction of ? to ? does not change any
  properties of ?.
• b. It behaves as if ? is not there, apart from
  semantic interpretation.
• c. is not the projection of any head.
• d. Adjuncts dont receive theta-roles or check
  morphological features.
• e. Cannot encode the argument-of relation
  correlated with head-complement dependencies.

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A window into an (almost) syntaxless mind

• Adjunction is, more positively
• additive iterative (stackable) unboundedly
• symmetrical
• compositional
• If we wish to motivate anything in syntax from
  conditions imposed by the semantic interface,
  adjuncts (an operation of predicate
  composition, Chomsky, 2004, 2005) are the place
  to look they LACK (MUCH) OF SYNTAX.
• A proto-language moreover would not need to
  contain anything else than adjunction.
• But there is no reference or truth in this system
  (that apparently needs more syntax).
• And there are no categories.

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A tight correspondence between one-dimensional
Merge (Add) and adjunction

• Adjunction of A to B does not change any
  properties of B
• and there is no projection of a new category
  under Merge (with or without labeling).
• Adjunction is symmetrical and unbounded
• and so is Merge.
• The putative asymmetry between the head and the
  adjunct (Chomsky, 2004) is simply not visible in
  a one-dimensional system.

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What else is on the other side?

• Most animals think but we are asking for the
  format of their thoughts.
• C-I incorporates a dual semantics, with
  generalized argument structure as one component,
  the other being discourse-related and scopal
  properties. (Chomsky, 2005)
• But are propositions waiting there to be
  expressed by language? Is there a pre-linguistic
  ability of intentional reference?
• Many reasons for scepticism (e.g. Terrace, 2005)

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What if there is no I-interface?

• No conceptual necessity that it exists all
  thats needed is that products of CS are usable
• I.e., some, and not necessarily all, of its
  information lends itself to certain purposes.
• Intentional reference increases in sophistication
  as structural complexity builds up incrementally.
• NP Caesars destruction of Syracuse
• vP Caesar destroy Syracuse
• TP Caesar destroyed Syracuse
• CP That Caesar destroyed Syracuse
• lion
• I ate D0 lion
• lions are tasty
• I ate a lion

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What if there is no C-interface?

• Argument structure
• Semantics is not conjunctive kill Bill does
  not mean ?ekilling(e) Bill(e)
• Involves integral (part-whole) relations between
  an event and its participants.
• Highly bounded, and in this sense not recursive.

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An overall internalist conclusion

• The semantic or extra-linguistic motivation of
  structural conditions of human thought stops at a
  point, as things get more syntactic.
• Whatever is beyond this point has to find an
  internalist explanation in the CS of language
  itself.
• Merge/Add has nothing to say about it.
• An internally productive syntax can be no more
  based on something with the algebraic properties
  of Succ than arithmetic can, being
  multi-dimensional.

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Explaining truth

• Truth is a human universal the best distributed
  good in the world (cf. Descartes, 1637, on the
  bon sens)
• As a concept unexplainable yet understood by
  everyone theory unneeded (why would a
  conceptual atom have a theory anyhow?).
• Theres adaptive behaviour, complex computation,
  functional reference, systematicity, etc., before
  any creature has thoughts about existence or
  truth.
• Applied by humans to anything that has the form
  of a (declarative) sentence, and to nothing that
  doesnt.
• The universal truth/reference distinction makes
  little semantic sense (Carstairs-McCarthy, 1999).

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The unthinkable?

• Emergence of the intentional - reference and
  truth through the functional layers of the
  clause?

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Syntax of integral predication of truth (Hinzen,
Truths Fabric, 2003)

• be DP
• Spec D
• D0 AgrP
• Spec Agr
• Agr 0 SC
• SPACE PRESENTATION

Intent- ional
Conce- ptual
truth
proposition
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Internalism about truth

• Truth cannot easily be integrated into the
  internalist framework (PMM Cecchetto 1997)
• But why?
• It is language-internally and structurally
  grounded (Hinzen, 2006c)
• not epistemically, communicatively, perceptually,
  or action-theoretically (as everyone holds).

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Summary

• The more we deflate our idea of what syntax does,
  we make ourselves hostage to an inflated idea of
  what externally imposed interface conditions can
  motivate.
• Return to a (more minimalist) use-theory of
  meaning.
• Language is not at least not wholly a
  linking system.
• The idea that structure-building in FL reduces to
  one-dimensional sequencing (Add) is very
  unlikely true, though that operation is part of
  the system, and possibly the true locus of
  recursion.
• The true locus of hierarchy, the argument
  structure system and the categories, resources
  are extremely limited
• 3 arguments
• 3 lexical categories
• 3 functional categories
• A derivation bottoms out conceptually
  intentionality comes later, as a function of the
  structure constructed.