In:Events, Arguments, and Aspects: Topics in the Semantics of Verbs
Edited by Klaus Robering
[Studies in Language Companion Series 152] 2014
► pp. 115–158
Abstract objects of verbs
Published online: 28 March 2014
https://doi.org/10.1075/slcs.152.03rob
https://doi.org/10.1075/slcs.152.03rob
Verbs do often take arguments of quite different types. In an orthodox type-theoretic framework this results in an extreme polysemy of many verbs. In this article, it is shown that this unwanted consequence can be avoided when a theory of “abstract objects” is adopted according to which these objects represent non-objectual entities in contexts from which they are excluded by type restrictions. Thus these objects are “abstract” in a functional rather than in an ontological sense: they function as representatives of other entities but they are otherwise quite normal objects. Three examples of such a representation are considered: the denotations of that-phrases are objects representing propositions, generic noun phrases denote objects standing for sorts, and infinitivals are viewed as denoting objects representing attributes, i.e., the “ordinary” meanings of verb phrases.
References (64)
Ackermann, Wilhelm (1950): “Widerspruchsfreier Aufbau der Logik, I.”
The Journal of Symbolic Logic
15: 33–57.
(1953): “Widerspruchsfreier Aufbau einer typenfreien Logik, II.”
Mathematische Zeitschrift
57: 155–166.
(1965): “Der Aufbau einer höheren Logik.”
Archiv für mathematische Logik und Grundlagenforschung
7: 5–22.
Anderson, Alan Ross & Belnap, Nuel D. (1975):
The Logic of Relevance and Necessity
. Vol. 1. Princeton and London: Princeton University Press.
Anderson, C. Anthony (1984): “General intensional logic.” In: Dov Gabbay & Franz Guenthner (eds.)
The Handbook of Philosophical Logic
, Vol. II, Dordrecht: Reidel. 355–385.
Boolos, George (1998a): “The iterative conception of set.” In: Boolos(1998b: p. 13–29). Originally published in
The Journal of Philosophy
68 (1971). 215–232.
Cantor, Georg (1890/91): “Über eine elementare Frage der Mannigfaltigkeitslehre.”
Jahresbericht der Deutschen Mathematiker-Vereinigung
1: 75–78. Reprinted: Cantor (1932: p. 278–281).
(1895): “Beiträge zur Begründung der transfiniten Mengenlehre.”
Mathematische Annalen
46: 481–512. Reprinted (together with the continuation of this article): Cantor (1932: p. 282–351).
(1932):
Abhandlungen mathematischen und philosophischen Inhalts
. Edited by Ernst Zermelo. Berlin: Springer. Reprinted: Hildesheim and New York: Olms 1966.
Chierchia, Gennaro (1982): “Nominalization and Montague grammar: A semantics without types for natural languages.”
Linguistics and Philosophy
5: 303–354.
(1988):
Topics in the Syntax and Semantics of Infinitives and Gerunds
. New York and London: Garland.
Cocchiarella, Nino B. (1987):
Logical Studies in Early Analytic Philosophy
. Columbus OH: Ohio State University Press.
Cochiarella, Nino B. (1986):
Logical Investigations of Predication Theory and the Problem of Universals
. Naples: Bibliopolis.
Curry, Haskel B. (1942): “The inconsistency of certain formal logics.”
The Journal of Symbolic Logic
7: 115–117.
Curry, Haskell B. & Feys, Robert (1958):
Combinatory Logic
. Vol. 1. Amsterdam: North-Holland Publishing Company.
Feferman, Solomon (1975): “Non-extensional type-free theories of partial operaions and classifications, I.” In: Justus Diller & Gert Heinz Müller (eds.) |= ISILC
Proof Theory Symposium. Dedicated to Kurt Schütte on the Occasion of His 65th Birthday
,Berlin, Heidelberg, and New York: Springer. 73–118.
(1984): “Toward useful type-free theories, I.” In: Robert L. Martin (ed.)
Recent Essays on Truth and the Liar Paradox
, Oxford:Clarendon Press.237–306. Also in:
The Journal of Symbolic Logic
. 49 (1984). 75–111.
Frege, Gottlob (1884):
Die Grundlagen der Arithmetik. Eine logisch-mathematische Untersuchung über den Begriff der Zahl
. Breslau: Koebner. Centenary edition. Hamburg: Meiner1986.
(1892): “Über Begriff und Gegenstand.”
Vierteljahresschrift für wissenschaftliche Philosophie
16: 192–205. Reprinted: Frege (1990: p. 167–178).
(1893/1903):
Grundgesetze der Arithmetik
. 2 Vols. Jena: Pohle. Reprinted: Hildesheim and New York: Olms 1966.
(1918/19): “Der Gedanke.”
Beiträge zur Philosophie des deutschen Idealismus
1: 58–77.
Reprinted: Frege (1990: p. 342–362). English translation: “The thought: A Logical Inquiry”. Mind 65 (1956). 289–311.
(1990):
Kleine Schriften
. Edited by Ignacio Angelelli. Hildesheim and New York: Olms, 2nd edition.
1st edition 1967.
(1962):
Reference and Generality. An Examination of Some Medieval and Modern Theories
. Ithaca NY and London: Cornell University Press. 3rd edition 1980.
(1967): “Identity.”
Review of Metaphysics
21. Reprinted: Geach, Thomas: Logic Matters. Oxford: Blackwell 1972. 2nd, corrected edition 1981. p. 238–247.
Groenendijk, Jeroen & Stokhof, Martin (1984): “Studies in the semantics of questions and the pragmatics of answers.” Ph.D. thesis, University of Amsterdam.
Grover, Dorothy L., Camp, Joseph L. & Belnap, Nuel D. (1974): “A prosentential theory of truth.”
Philosophical Studies
27: 73–125.
Gupta, Anil (1980):
The Logic of Common Nouns. An Investigation in Quantified Modal Logic
. New Haven and London: Yale University Press.
Hale, Bob (2001): “Singular terms (1), (2).” In: Hale & Wright (2001: p. 31–47 (1), 48–71 (2)).
Hale, Bob & Wright, Crispin (eds.) (2001):
The Reason’s Proper Study. Essays towards a Neo-Fregean Philosophy of Mathematics
. Oxford: Oxford University Press.
Hindley, J. Roger & Seldin, Jonathan P. (1986):
Introduction to Combinators and λ-Calculus
. Cambridge GB: Cambridge University Press.
Hiż, Henry (1984): “Frege, Leśniewski and information semantics on the resolution of the antinomies.”
Synthese
60 : 51–72.
Keenan, Edward L. & Faltz, Leonard M. (1985):
Boolean Semantics for Natural Language
. Dordrecht: Reidel.
Meschkowski, Herbert (1967):
Probleme des Unendlichen. Werk und Leben Georg Cantors
. Braunschweig: Vieweg.
Montague, Richard (1970): “Universal grammar.”
Theoria
36: 373–398. Reprinted: Thomason (1974: p. 222–246).
(1973): “The proper treatment of quantification in ordinary English.” In: Jaakko Hintikka, Julius Moravcsik & Patrick Suppes (eds.)
Approaches to Natural Language
:
Proceedings of the 1970 Stanford Workshop
,Dordrecht: Reidel. 221–242. Reprinted: Thomason (1974: pp. 247–270).
Morrill, Glyn V. (1994):
Type Logical Grammar. Categorial Logic of Signs
. Dordrecht, Boston, London: Kluwer.
Myhill, John (1963): “An alternative to the method of extension and intension.” In: Paul Arthur Schilpp (ed.)
The Philosophy of Rudolf Carnap
, La Salle IL: Open Court. 299–310.
Quine, Willard Van Orman (1940):
Mathematical Logic
. Cambridge MA: Harvard University Press. Revised Edition 1951.
(1953): “New foundations for mathematical logic.” In:
From a Logical Point of View. 9 Logico-Philosophical Essays
. Cambridge MA: Harvard University Press. 80–101.
Ramsey, Frank P. (1927): “Facts and propositions.”
Aristotelian Society Supplementary
VolumeVII: 153–170. Reprinted: Ramsey, Frank P.: Foundations. Essays in Philosophy, Logic, Mathematics and Economics. Ed. by D. H.Mellor. London: Routledge and Kegan Paul 1978. 40–57.
Robering, Klaus (1994): “Stufen, Typen, Sorten.” In: Klaus Robering (ed.)
Sorten, Typen, Typenfreiheit. Probleme der Klassifikation semantischer Einheiten
,Berlin: Technische Universität Berlin. 5–55.
(2000): “Categorial graph grammar: A direct approach to functor-argumentor structure.”
Theoretical Linguistics
26: 31–73.
(2008): “Ackermann’s class theory.” In: Klaus Robering (ed.)
New Approaches to Classes and Concepts
, London: College Publications. 23–56.
Scott, Dana (1971): “The lattice of flow diagrams.” In: Erwin Engeler (ed.)
Symposium on Semantics of Algorithmic Languages
, Berlin, Heidelberg, New York: Springer. 311–372.
Specker, Ernst P. (1953): “The axiom of choice in Quine’s ‘New Foundations for Mathematical Logic’.”
Proceedings of the National Academy of Sciences
39.
Thomason, Richmond (ed.) (1974):
Formal Philosophy. Selected Papers by Richard Montague
. New Haven: Yale University Press.
