An Introduction to Radical Minimalism

Merge, Agree & Transfer Revisited

Diego Gabriel Krivochen (UNLP / Universität Potsdam)

Basic Tenets of Radical Minimalism1. 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:

The Strong Radically Minimalist ThesisAll 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.

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.

On MergeMerge 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.

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.

Types of MergeMerge (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

On FormatOntological 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.

Derivational DynamicsMerge 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.

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

On AgreeStandard 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

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)

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.

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.

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).

Structurally…

α

γ β [ψ-D]

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.

On TransferChomsky (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.)

Problems

Massive amount of Look Ahead

Stipulative definition of transferrable objects: v*Ps and CPs (PPs, DPs are conflictive)

Passive interfaces

An alternative: Invasive InterfacesTransfer 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:

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.

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]}}}

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.

Thanks for your attention!