Talk delivered in Adam Mickiewicz-University (Poznan, Poland) and Potsdam University (Germany). More details in papers available online.

1. Merge, Agree & Transfer Revisited
Diego Gabriel Krivochen (UNLP / Universität Potsdam)

2. Basic Tenets of Radical Minimalism
1. Language is part of the “natural world”; therefore, it is
fundamentally a physical system.
2. As a consequence of 1, it shares the basic properties of
physical systems and the same principles can be applied,
the only difference being the properties of the elements
that are manipulated in the relevant system.
3. The operations are taken to be very basic, simple and
universal, as well as the constraints upon them, which are
determined by the interaction with other systems, not by
stipulative intra-theoretical filters.
4. 2 and 3 can be summarized as follows:

3. The Strong Radically Minimalist Thesis
 All differences between physical systems are
“superficial” and rely only on the characteristics of their
basic units [i.e., the elements that are manipulated],
which require minimal adjustments in the
formulation of operations and constraints [that is,
only notational issues]. At a principled level, all
physical systems are identical, make use of the same
operations and respond to the same principles.

4. Principles:
 Conservation Principle: Dimensions cannot be
eliminated, but they must be instantiated in such a way
that they can be read by the relevant level so that the
information they convey is preserved.
 Dynamic (Full) Interpretation: any derivational step
is justified only insofar as it increases the
informational load and/or it generates an interpretable
object.

5. On Merge
 Merge is a free unbounded operation that applies to
two (smallest non-trivial number of elements) distinct
(see below) objects sharing format, either ontological
or structural. Merge is, on the simplest assumptions,
the only generative operation in the physical
world.

6. Formally:
 Merge is a concatenation function, derived from
conceptual necessity.
 Concatenation defines a chain of coordinates {(x, y,
z…n)WX … (x, y, z…n)WY…(x, y, z…n)Wn} where WY ≡
WX ≡ Wn or WY ≠ WX ≠ Wn. If WX ≠ WY, they must be
isodimensional.

7. Types of Merge
 Merge (α, β), α ≠ β –but α and β share format-
Distinct binary Merge (Boeckx, 2010a; Krivochen,
2011b, c)
 Merge (α, β), α = β Self Merge (Adger, 2011)
 Merge (α, β, γ…), α ≠ β ≠ γ Unrestricted distinct
Merge

8. On Format
 Ontological format refers to the nature of the entities
involved.
 Structural format refers to the way in which elements
are organized.
 Ontological format is a necessary condition for Merge
to apply: the resultant structures will always consist on
formally identical objects.

9. Derivational Dynamics
 Merge manipulates Tokens from a Type-Array.
 LEXS is the full set of type-symbols that can be
manipulated by a computational system S, which is a
generative W.
 An array is a set of types drawn from LEXS.
 A token is an occurrence of a type within WX. There are
no a priori limits to the times a type can be
instantiated as a token but those required by Interface
Conditions IC.

10. A lexical item LI is a structure {X…α…√} ∈ WX, where
X is a procedural category (D, T, P), α is a n number of
non-intervenient nodes for category recognition
purposes at the semantic interface, and √ is a root.
[D…α…√] = N
[T…α…√] = V
[P…α… √] = A, Adv

11. On Agree
 Standard Agree (Chomsky, 1998, 1999; Pesetsky &
Torrego, 2004, 2007): Unvalued feature(s) F in probe
search for closest valued instance of F in the goal
within its c-command domain. Top-down search.
 “Reverse” Agree (Wurmbrand, 2011, Zeijlstra, 2011): The
higher element values F in the lower one, provided
that both are in the same phase

12. Problems:
 Features and values substantively complicate the theory. Elements
are assigned valued-interpretable / unvalued-uninterpretable
features arbitrarily. What is more, some features are introduced into
the derivation with the sole purpose of “explaining” certain
operations (e.g., EPP in T or Wh- in C), and be then erased.
 There is no reason, beyond theory-internal stipulation (for the sake
of Agree), for the same “feature” to be present in two different
locations, the probe and the goal.
 The very definition of feature is not clear: Uriagereka (comments to
Chomsky, 1999) defines them as valued dimensions. However, we
find:
Binary features: [± D] (e.g., Number)
Multiple-value features: [α D], [β D], [γ D] (e.g., Case)
No-value features: [F] (e.g., EPP, Wh-, EF)

13. An Alternative: Collapse
 A physical system changing linearly:
α α’ β β’
Since α and β are possible states of the system, so is their arbitrary linear
combination aα + bβ. What Schrödinger’s Equation (SE) tells us is that given
that α and β would change in the ways just indicated, their linear combination
must also change in the following way:
aα + bβ aα’ + bβ’.
These equations only hold if no “measurement” is taking place.
If a “measurement” is taking place then we must consider an entirely different
story: during the measurement, the system S must “collapse” into a state that is
certain to produce the observed result of the measurement.

14. How to apply this to Language?
 Let us assume the framework outlined so far and the
following quantum dimension: [CaseX]. This dimension
comprises three possible “outcomes”: NOM sphere (φ),
ACC sphere (θ) and DAT sphere (λ). All three are possible
final states of the system, and therefore the linear
combination must also be considered a legitimate state of
the system. The dimension in abstracto could then be
expressed as follows, using SE:
 Nφ + Aθ + Dλ
The factor that makes the relevant dimension collapse is
the merger of a functional / procedural node.

15. Definition:
 Collapse: α collapses a quantum
dimension [ψ-D] on β –being α a procedural
category and β a root or extended projection-
iff α has scope over β, the procedural
instructions conveyed by α are specified
enough as regards distribution and there is a
local relation between α and β (there is no γ
closer to β than α that can collapse a
dimension on β).

16. Structurally…
α
γ β
[ψ-D]

17.  No features, just dimensions –the semantically interpretable
part- comprising –in abstracto- all possible outcomes (ψ-state).
Final product is strictly componential and determined by local
relations and cumulative influence. Collapse, contrarily to
Agree, is a strictly interface-required operation, and no ad hoc
element is introduced in the working area to make it work.
 No constraints on Merge (Cf. Agree).
 α - β relation is interface-determined, as syntax can manipulate
quantum dimensions on their ψ-state. Locality is presupposed,
if α can collapse a quantum feature on β, it is because β has not
been transferred yet and γ is not an intervenient node. As soon
as a “suitable” procedural node is merged, collapse takes place,
even though there is no unidirectional influence determined a
priori, we work with “areas of influence”, so that elements in
local domains are in permanent interaction in the interfaces, as
interpretation is performed in real-time.
 Erasure of features is banned because of the Conservation
Principle: information cannot be lost, only gained or
transformed.

18. On Transfer
 Chomsky (2007: 11): “(…) optimal computation
requires some version of strict cyclicity. That will
follow if at certain stages of generation by repeated
Merge, the syntactic object constructed is sent to
the two interfaces by an operation Transfer, and
what has been transferred is no longer accessible to
later mappings to the interfaces (the phase-
impenetrability condition PIC). Call such stages
phases.” (emphasis, N.C.)

19. Problems
 Massive amount of Look Ahead
 Stipulative definition of transferrable objects: v*Ps and
CPs (PPs, DPs are conflictive)
 Passive interfaces

20. An alternative: Invasive Interfaces
 Transfer is the operation via which an Interface Level
ILX takes a fully interpretable object from W to
proceed with further computations.
 Corollary: if WX interfaces with more than one IL,
Transfer applies for each IL separately.
 Analyze evaluates the objects built via Merge in WX in
order to verify full interpretability in ILX.
 This leads to a dynamic definition of phase:

21. On Phases:
 PW is a phase in W if and only if it is the
minimal object fully interpretable in IL.
 Analyze applies after every derivational step, but the
generation of “momentarily” illegible structures can be
tolerated because of Soft Crash.

22. Sample derivational steps
 NS Merge (D[CaseX], √) = {D, √}
 C-I2 Label {D[CaseX], √} = {D, {D[CaseX], √}} This {D} will
be taken as a unit for the purpose of future operations.
Incidentally, {D[CaseX], √} “categorizes” √ as N, following
our definition.
 C-I2 Analyze: not fully interpretable unit: D has a
quantum dimension in its ψ-state.
 NS Merge (P, {D[CaseX]}) = {P, {D[CaseX]}} P’s procedural
instructions collapse [CaseX] on {D} to DAT sphere.
 C-I2 Label {P, {D[DAT]}} = {P, {P, {D[DAT]}}}

23.  C-I2 Analyze: {D}’s referential properties depend on
the cumulative influence of Time, Aspect and
Modality. Not fully interpretable yet. Relational
element P requires another element (a figure).
 NS Merge (D[CaseX], √) in parallel to (1) = {D[CaseX], √}
Labeling and Analyzing also take place. No procedural
head can collapse {D}’s Case dimension, so the
structure is not yet fully interpretable.
 NS Merge by Structural Format ({D}, {P, {P, {D}}}) =
{{D}, {P, {P, {D}}}}
 C-I2 Label {{D}, {P, {P, {D}}}} = {P}.
 C-I2 Analyze: {D} has a [CaseX] quantum dimension
still uncollapsed. Not fully interpretable. Therefore, P
is not interpretable either.