# Complex Cardinal Numerals and the Strong Minimalist Thesis

## Abstract

**:**

## 1. Purpose

_{,}2005 [3], et seq.) for the development of an explanatory theory of the language internal to the mind (I-language) able to derive the syntactic properties of linguistic expressions and the instructions they provide to the external systems for their interpretation.

- (1)
- a. hundred twob. hundred and two
- (2)
- a. two hundredb. two hundred thousand
- (3)
- a. hundreds of thousands of millionsb. hundreds of thousands of millions of trillions
- (4)
- a. centodue, cento e due (I)“hundred two”, “hundred and two”b. duecento, duecentomila“two hundred”, “two hundred thousand”c. centinaia di migliaia di milioni“hundreds of thousands of millions”

- (5)
- duo de viginti, un de viginti (L)two DE twenty, one DE twenty“eighteen”, “nineteen”
- (6)
- diciasette, diciotto, dicianove (I)ten seven, ten eight, ten nine“seventeen”, eighteen”, “nineteen”

## 2. Minimalist Program and Strong Minimalist Thesis

- (7)
- eM: (α, β): {α, β}iM: (α, {{
~~α~~, β}): {α{~~α~~, β}}

- (9)
- Condition on Spell-Outa. Edge(x) must be phonetically overt.b. The condition in (a) applies in a minimal way so that eitherthe Head or the Specifier, but not both, are spelled out overtly.(Collins 2007: 3)

## 3. A Minimalist Approach

#### 3.1. Language and Arithmetic

#### 3.1.1. Merge/Successor Function

- (11)
- a. 0 is in N.b. If n is in N, then n+1 is in N.

- (12)
- Counting and the successor function1= {LI}, 2= {LI, {LI}}, 3 = {LI, {LI, {LI}}}, …

#### 3.1.2. Merge/Boolean Algebra

#### 3.1.3. Language Variation

#### 3.2. Minimal Structures

- (20)
- a. hundred and twob.*and hundred twoc *hundred two and
- (21)
- a. thousands of millionsb.*of thousands of millionsc. *thousands millions of

- (22)
- a. NumP Co NumPb. *Co NumP NumPc. *NumP NumP Co

#### 3.3. Extended Projection

- (30)
- a. hundreds of thousands of millionsb. hundreds of thousands of millions of trillions
- (31)
- a. dizaines de centaines de milliers de millions (F)b. dizaines de centaines de milliers de millions de trillions
- (32)
- a. two million two hundred and thirty-twob. two trillion two million two hundred and thirty-two
- (33)
- ...

- [41]

- (35)
- a. John met and John and Mary.b. John met both John and Mary.c. John met both and John and Mary.

- (36)
- ...

#### 3.4. Instructions to SM

_{[uNum]}>, (37b). At the third step, Co

_{{[uNum], [ADD]}}taken from the lexicon is e-merged to the precious constituent, (37c). At the fourth step, NumP

_{[Num]}is internally merged to the previously derived constituent and values the [uNum] feature of Co

_{{[uNum],[ADD]}.}Given PM, the copy of the displaced NumP is not pronounced. COS applies, and given that the Specifier is pronounced, the higher Co head is not pronounced <Co

_{{[uNum], [ADD]}}>, see (37d). When Co is pronounced, as in twenty and one, PM and COS apply after the displacement of Num, and the lower Co is pronounced, see (38d).

#### 3.5. Instructions to CI

- (44)
- a. Twenty-one is a natural number.b. *Twenty and one is a natural number.
- (45)
- a. *Twenty-one are natural numbers.b. Twenty and one are natural numbers.
- (46)
- a. Both twenty and one are natural numbers.b. *Both twenty-one are natural numbers.
- (47)
- a. *Only twenty and one is a natural number.b. Only twenty-one is a natural number.

- (48)
- a. The mother and child are/*is in the garden.b. The lion-leopard *are/is in the garden.
- (49)
- a. This mother and child are often together.b. ≈This lion-leopard are often together.
- (50)
- a. Both mother and child are in the garden.b. ≠Both lion-leopard are in the garden.
- (51)
- a. ≠Only the mother and child is in the garden.b. Only the lion-leopard is in the garden.

_{[D]}[ Co

_{[G]}[ Co

_{[I]}[ Co

_{[L]}[ Co. It might be the case that operator features, such as [ADD] and [MULT], occupy higher regions in the extended projection or sub-projections of Co and emerge at later stage in language acquisition. These questions will be left to further research.

#### 3.6. Section Summary

## 4. Previous Analyses

#### 4.1. Phrase Structure Rules

- (54)
- a. NUM → DIGITb. NUM → NUMPHRASEc. NUM → NUMPHRASE NUMd. NUMPHRASE → NUM M

#### 4.2. Regular Syntactic Rules and Type Theoretic Semantics

^{0}head is associated with phi-features, [±Plur], which play a role in the agreement relation between the numeral complex in Specifier position of NumP and the nominal constituent in the Complement position. See Kayne (2016) [58] and Cinque (2022) [59] for the syntactic projection of numeral classifiers. See Krifka (1995) [60] and Chierchia (1998) [61] for different approaches to numeral classifiers.

- (56)
- a. six feet six inches of finest silkb. six feet and six inches of finest silk
- (57)
- a. two dollars (and) seventy-five centsb. two dollars (and) seventy-five
- (58)
- a. une heure (et) trente (F)one hour (and) thirty“one thirty”b. une heure (et) trente minutesone hour (and) thirty minutes“one thirty”

#### 4.3. Section Summary

## 5. Conclusions

## Funding

## Conflicts of Interest

## Notes

1. | In the Minimalist Program (Chomsky 1995 et seq.), category-specific rules, postulated in previous stages of the theory of Generative Grammar are subsumed under Merge. This includes phrase structure rules (Chomsky 1965), and phrase structure rule schemata (X-bar Theory), as well as transformations, such as Move NP, which applies for example in the derivations of passive structures, and Move-wh, which applies for example in the derivation of questions in the Government and Binding model (Chomsky 1981), as well as Head Movement, which displaces a syntactic Head to a higher Head position in a syntactic derivation. Specific constraints on the application of these rules, such as the Head Movement Constraint, the Strict Cycle, the Extension Condition, now follow from the strictly Markovian nature of syntactic derivations. See Chomsky (2019) for discussion. |

2. | A further distinction between Set-Merge and Pair-Merge was introduced in Chomsky (2000), to capture argument-adjunct asymmetries. Set-Merge derives unordered sets, {x,y} and yields the symmetrical property of complementation (arguments), while pair-Merge derives ordered sets, <x,y> and yields the asymmetric property of adjunction (modifiers). The distinction between Set-Merge and Pair-Merge gives rise to issues, which are beyond the scope of this article. See for example, Omune, J. 2015. Immediate-local Merge as, Pair-Merge. Coyote Papers. University of Arizona Circle 22:12-21. Oseki, Y. 2015. Eliminating Pair-Merge. Proceedings of the 32nd West Coast Conference on Formal Linguistics: 303-312. Somerville, MA: Cascadilla Proceedings Project. Somerville, MA, USA. Kitahara, H., M. Nomura, M. Oishi. J. Omune. 2019. Pair-Merge Under Merge. (Chomsky 2019, 2021). |

3. | AGREE is the operation responsible for moving feature values from one element to another, and thus provides a tool to model dependencies between syntactic constituents in the structure they are part of. Syntactic constituents are associated with valued ([F]) and unvalued ([uF]) features. Unvalued features must be valued before the interfaces to satisfy Full Interpretation. Feature valuation between a probe and a goal is done via minimal search, where the probe sister-contains its goal, and according to our view, also falls into third factor principles external to the language faculty. |

4. | According to Derivation by Phases, a phase is a unit of syntactic computation that exhibits independence at the interfaces. Phases are transferred to the interfaces when the next higher phase is completed. Phase Theory subsumes several constraints on syntactic derivations proposed in earlier stages of Generative Grammar, and according to our view, also falls into principles external to the language faculty. |

5. | See B. H. Partee, Alice ter Meulen and R.E. Wall. 1993 Mathematical Methods in Linguistics. Studies in Linguistics and Philosophy. Dordrecht, Kluwer, for discussion on proof theoretical as well as declarative constructions of the set of natural numbers. I thank an anonymous reviewer for this reminder. |

6. | NumP is a syntactic projection standing for numeral phrase. NumP is located between DP and NP in the extended nominal projection: as discussed in Cinque (2005), Rizzi and Cinque (2016), and Cinque (2022) among other works. |

7. | Many thanks to Mohamed Guerssel for providing examples of multiplicative complexes in Arabic. |

8. | As mentioned by an anonymous reviewer, the fact that the position and function of conjunctions, such as and, and prepositions, such as of, is the same in numeral structures is not to be unexpected. From our perspective, these elements are both functional heads, thus they occupy the same structural position. The coordinate conjunction does not project its label, this can also be the case for the grammatical formative of. Like prepositions, and other functional categories, conjunctions have extended projections, see Section 3.3, as well as Di Sciullo (2020) and (2021) for discussion. |

9. | For example, one hundred thousand is/*are a natural number vs. hundreds of thousands *is/are (a) natural numbers. |

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**MDPI and ACS Style**

Di Sciullo, A.M.
Complex Cardinal Numerals and the Strong Minimalist Thesis. *Philosophies* **2022**, *7*, 81.
https://doi.org/10.3390/philosophies7040081

**AMA Style**

Di Sciullo AM.
Complex Cardinal Numerals and the Strong Minimalist Thesis. *Philosophies*. 2022; 7(4):81.
https://doi.org/10.3390/philosophies7040081

**Chicago/Turabian Style**

Di Sciullo, Anna Maria.
2022. "Complex Cardinal Numerals and the Strong Minimalist Thesis" *Philosophies* 7, no. 4: 81.
https://doi.org/10.3390/philosophies7040081