Philosophy and Logic of Predication

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Contributors

Ignacio Angelelli
The University of Texas at Austin, USA
angelelli@utexas.edu

Allan Bäck
Kutztown University, Pennsylvania, USA
back@kutztown.edu

Nino B. Cocchiarella
Indiana University, USA
cocchiar@indiana.edu

Danny Frederick
Slate House, Hunstan Lane, Old Leake, Boston, UK
dannyfrederick77@gmail.com

Peter Hanks
University of Minnesota, USA
pwhanks@umn.edu

Bjørn Jespersen
VSB-Technical University of Ostrava, Czech Republic
bjorn.jespersen@gmail.com

David Liebesman
University of Calgary, Canada
david.liebesman@gmail.com

António Pedro Mesquita
University of Lisbon, Portugal
apmesquita@netcabo.pt ← 7 | 8 →

Jacek Paśniczek
Maria Curie-Skłodowska University, Lublin, Poland
jpasnicz@bacon.umcs.lublin.pl

Piotr Stalmaszczyk
University of Łódź, Poland
piotrst@uni.lodz.pl

Mieszko Tałasiewicz
University of Warsaw, Poland
m.talasiewicz@uw.edu.pl

← 8 | 9 →

Piotr Stalmaszczyk

University of Łódź

Predication Theory: Introduction

It is no news that a theory of predication is no sooner formulated than it generates puzzles.
Wilfrid Sellars “Towards a Theory of Predication” (1985)

1.   Predication Theory

Research in linguistics, philosophy of language, ontology, metaphysics, and logic makes ample, both explicit and implicit, use of the concept of predication. In the words of Ignacio Angelelli predication has been and continues to be the central topic of logic and ontology (or metaphysics) in the entire history of philosophy, from Antiquity till now (Angelelli, this volume); whereas for Nino Cocchiarella “predication has been a central, if not the central, issue in philosophy since at least the time of Plato and Aristotle” (Cocchiarella 1989: 253), and for John Searle, within a different theoretical and methodological frame, “predication, like reference, is an ancient (and difficult) topic in philosophy” (Searle 1969: 97). The following overview very briefly mentions some of the most important approaches to predication and predication theory, especially in the context of the articles collected in this volume.

In traditional grammar, predication is the relation between the subject and the predicate. In logic, predication is the attributing of characteristics to a subject to produce a meaningful statement combining verbal and nominal elements. This understanding stems from Aristotelian logic, where the term (though not explicitly used by the philosopher) might be defined as “saying something about something that there is”.¹

In logical inquiries, this classical definition is echoed in more recent investigations by the ‘thing-property’ relation holding in appropriate propositions (e.g. in Reichenbach 1947). According to Quine (1960), predication is the basic combination in which general and singular terms find their contrasting roles: ← 9 | 10 → “Predication joins a general term and a singular term to form a sentence that is true or false according as the general term is true or false of the object, if any, to which the singular term refers” (Quine 1960: 96); Quine also considers predication to be one of the mechanisms which join occasion sentences. Quine’s treatment of predication is characteristic of most logical approaches in being bipartite, i.e. it focuses on the (contrasting) roles of two elements in the relation (disregarding the importance of a possible triggering operator), it also distinguishes monadic and polyadic predication.

The above ideas are close to Lorenzen’s (1968) observation concerning ‘basic statements’ (Grundaussagen), the simplest structures of a language which are composed of a subject and a predicate. Strawson (1971) stresses that predication is an assessment for truth-value of the predicate with respect to the topic, similarly Searle (1969), who also provides a speech act theory of predication, observing that it is not a separate speech act at all.² According to Link (1998) predication is the basic tool for making judgments about the world, it relates predicates and individual terms to form sentences, semantically “that means that some individuals are said to have properties or to stand in relation to one another” (Link 1998: 275).³

Predication can be also understood as the nexus between a subject and a predicate expression (Chierchia 1985; Cocchiarella 2013), the basis of the unity of a speech act (Cocchiarella 2013; this volume). For Victor Dudman “a theory of predication for a language is meant to explain what can be said in it, and how” (Dudman 1985: 43). On the other hand, Sellars (1985, §83) stresses the necessity of distinguishing “the psychological and the logical dimensions of predication), and Cocchiarella (2013: 302) distinguishes “the nexus of predication in reality that is part of this natural realism from the nexus of predication in our speech and mental acts”.⁴

The traditional grammatical approach to predication, with the division of the clause (or simple sentence) into two basic constituents: subject and predicate, ← 10 | 11 → can be seen in, among others, Bloomfield’s (1933) analysis of ‘favorite sentence-forms’, and Hockett’s (1958) operation of conjoining. However, Jespersen (1937) abandoned the term altogether, and instead introduced the concept of nexus, a relation joining two ideas, justifying his decision in the following way:

It would probably be best in linguistics to avoid the word predication altogether on account of its traditional connexion with logical theories. In grammar we should, not of course forget our logic, but steer clear of everything that may hamper our comprehension of language as it is actually used; this is why I have coined the new term nexus with its exclusive application to grammar (Jespersen 1937: 120).

Terminological considerations notwithstanding, Jespersen’s conception of predication is explicitly bipartite and firmly relational: a predication is established by some specific combination of what becomes the subject and the predicate, or, in somewhat looser terms, “something happens in a nexus” (Jespersen 1937: 121).

Krifka (1998) claims that a predication establishes a relation of a specified type between a number of parameters, or semantic arguments. For example, sentences with intransitive verbs establish a relation that holds of the subject for some event, and sentences with transitive verbs establish a relation that holds between the subject, the object, and some event.

In Davidson’s approach to verb semantics predication can be specified as a relation between a verb and one of its semantic entailments (Davidson 1967), or as a combinatory relation which makes it possible to join a property and an argument of the appropriate semantic type to form a formula whose truth or falsity is established according to whether the property holds of the entity denoted by the argument or not. Elsewhere Davidson related predication to the problem of ‘the unity of proposition’ and claimed that “(…) if we do not understand predication, we do not understand how any sentence works, nor can we account for the structure of the simplest thought that is expressible in language” (Davidson 2005: 77).⁵

Early generative grammar, in the Chomskyan tradition, paid very limited attention to the notion, and later studies, e.g. Williams (1980) and Rothstein (1985, 1992), viewed predication as a primitive syntactic relation. Whereas Williams argued for an indexing approach and almost equaled predication with semantic role assignment, Rothstein claimed that the semantic and syntactic concepts of predication are distinct, and the relation which holds between predicates and ← 11 | 12 → subjects at S-structure can be defined in purely syntactic terms. Higginbotham (1987) understands predication as a formal binary relation on points of phrase markers, and Bowers (1993) postulates the existence of a functional category responsible for implementing the relation.⁶ Cinque (1992) observes that in the generative approach to linguistic analysis an abstract predication relation underlies all sentences, even those lacking a genuine semantic predication and presentational sentences.

In the Government and Binding model of generative grammar, the obligatory presence of the closing argument (subject) in a subject-predicate structure follows from the second clause of the Extended Projection Principle (EPP).⁷ Later, Chomsky (1986) suggested that this part of the EPP might be derived from the theory of predication, as developed in Williams (1980) and Rothstein (1985), and observed that the EPP “is a particular way of expressing the general principle that all functions must be saturated” (Chomsky 1986: 116). Chomsky explicitly referred to Frege, and observed that a maximal projection (e.g. VP or AP) may be regarded as a syntactic function that is “unsaturated if not provided with a subject of which it is predicated” (Chomsky 1986: 116).⁸

2.   Types of Predication

According to Meixner (2009: 199) “Prior to Frege, there was no philosophically adequate theory of predication (…) Frege, in the nineteenth century, brought the philosophy of predication on the right track”.⁹ Gottlob Frege has been commonly credited with proposing a bipartite analysis of expressions into a functor and its ← 12 | 13 → argument(s). His approach to predication, understood here as a primitive logical relation, may be thus termed functional: a function has to be saturated by an argument.¹⁰ Fregean approach contrasts thus with the concatenative approach to predication, rooted in the Aristotelian tradition. Both these approaches find application in modern theories – linguistic and philosophical – of language.¹¹

2.1   Aristotelian Predication

In Aristotelian semantics, predication is the relation constituted by two elements, the subject with the predicate, with tense specification being a third, concatenating, element, as in the following formula:¹²

Aristotelian predication:
Proposition ⇒ Subject^ᴖTense^ᴖPredicate

Whereas predication in grammatical theory is concerned with linguistic items, Aristotle was concerned with relations between entities in the ontology, it is ← 13 | 14 → therefore necessary to distinguish between reference to linguistic items, i.e. linguistic predication, and reference to items in the ontology, i.e. ontological predication:¹³

Linguistic predication:
A predicate (a linguistic item) is linguistically predicated of its subject (a grammatical item).

Ontological predication:
A predicable (a metaphysical item) is ontologically predicated of its subject (an item in the ontology).

Two relations which are variants of metaphysical/ontological predication are introduced by Aristotle in the Categories:¹⁴

(1) and (2) exemplify the relations holding between items in the ontology: between a metaphysical subject, Socrates, and a predicable, man or pallor. ‘SAID OF a subject’ is a relation of ontological classification, ‘IN a subject’ is a relation of ontological dependence. Furthermore, (1i) tells us something fundamental about what kind of thing Socrates is, it is therefore an example of essential predication. On the other hand, (2i) tells us something that happens to be the case, it is an example of accidental predication. In (1ii) and (2ii) the linguistic predication is related to ontological predication, however, Aristotle is concerned primarily with giving the metaphysical configurations that underlie sentences (1i) and (2i), and, as pointed out by Lewis (1991: 55), the philosopher is silent on how the two kinds of predication are related. As observed by Lewis (1991: 4, n.4), the relation between linguistic predication and metaphysical predication is not bi-directional: the subject of a linguistic predication can be either a linguistic item or an entity in the ontology, however the subject of a metaphysical predication will always be an ontological item, and not a linguistic one.

A similar point is made by Mesquita (this volume), who stresses the necessity to distinguish two levels in Aristotelian thought: “the ontological level, where ← 14 | 15 → we speak of predicates as something that pertains to things; and the logical level, where we speak of predicates as something that is said of things”. In the former case the predicate is an entity ‘utterly extra-logical and extra-linguistic’, in the latter the predicate is a term, a part of a sentence, hence a linguistic item.

2.2   Fregean Predication

In Fregean semantics the application of a function to an argument is not a mere juxtaposition of the two elements. The function combines with the argument into a self-contained whole due to the fact that it contains a logical gap (the place-holder, or argument-place) which needs filling. As concluded by Frege in “Über Begriff und Gegenstand” (‘On Concept and Object’, 1892): “not all the parts of a thought can be complete; at least one must be unsaturated or predicative; otherwise they would not hold together” (Frege [1892]: 193). Tichý (1988: 27) comments, somewhat metaphorically, that “the function latches on its argument, sticking to it as if through a suction effect”.

Thus, in Fregean semantics, predication is a relation in which an argument saturates an open position in the function, cf. the simplified formula below:

Fregean predication:
Proposition ⇒ [Function (1, …, n)] ^ᴖArgument_{(1, …, n)}

It needs to be stressed at this point that Fregean semantics is not concerned with natural language predicates. His line of reasoning, however, may be applied to analyzing predication as a grammatical relation. The above formula aims at capturing Tichý’s observation that “the function latches on its argument”, furthermore, the “suction effect” is attributed to the presence of the open position(s) – ‘(1, …, n)’. I use above the term “Proposition” as a generalized term for Frege’s “act of judgement” and “assertion”.¹⁵ As observed by Stevens:

Rather than analyzing the proposition into a series of elements (subject, predicate, copula), Frege construes the predicative part of the proposition as a function which is essentially incomplete or ‘unsaturated’. (Stevens 2003: 224)

In other words, there is a need for a predicative constituent in a proposition to bind the propositional content into a ‘fully-fledged unit’, cf. Stevens (2003: 230–231). ← 15 | 16 →

Paul Pietroski remarked that Frege “bequeathed to us some tools – originally designed for the study of logic and arithmetic – that can be used in constructing theories of meaning for natural languages” (Pietroski 2004: 29–30). These ‘Fregean tools’ still prove useful in analyzing not only the fundamental issues of sense and reference, but also such notions as predication, predicate, argument and concept, as demonstrated by the chapters in Part Two of this volume, and Frege’s “philosophy of language […] remains intensely vital today. Not since medieval times has the connection between logic and language been so close” (Mendelsohn 2005: xviii).

Contributions gathered in this volume discuss the philosophy and logic of predication, they focus on the Aristotelian model and its legacy, and also on Fregean predication, its limits and possible refinements.

3.   Contents of the Volume

The volume is divided into two parts: papers in Part One are concerned with historical investigations, albeit with considerable importance for contemporary research on predication theory and implications for the future. Contributions in Part Two discuss philosophical and more formal topics, including an algebraic approach to Meinongian predication, and tackle some controversial issues stemming from Fregean semantics.

Predication is a complex entity in Aristotelian thought. António Pedro Mesquita attempts to provide an account for this complexity, starting with a crucial chapter of the Posterior Analytics (I 22), where, in the most complete and developed manner within the corpus, Aristotle proceeds to systematize this topic. It follows from the analysis that predication can assume, generically, five forms: the predication of essence (that is of the genus and the specific difference); essential predication (that is either of the genus or of the differences or their genera); the predication of accidents per se; the predication of simple accidents; and accidental predication. Mesquita observes that only some types are forms of strict predication (ἁπλῶς), and he concludes with a discussion of Aristotle’s thesis according to which no substance can be a predicate, which is implied by its notion of accidental predication, a thesis which has been (wrongly so in the author’s opinion) challenged in modern times.

Nino B. Cocchiarella offers a conceptualist view on predication. He starts with observing that predication can be also understood as the nexus between a subject and a predicate expression, the basis of the unity of a speech act, including speech acts in the plural and speech acts that involve mass nouns. And a speech act, of course, is an overt expression of a mental act, e.g., a judgment; and therefore ← 16 | 17 → the unity of a speech act such as an assertion is really the unity of the judgment that underlies that act. Such a mental act, and therefore the speech act as well, has a unity based on how the referential and predicable roles of the subject and predicate expressions combine and function together respectively. Cocchiarella proposes to explain this unity of predication in terms of a conceptualist theory of logical forms that, as he claims, underlies at least some important aspects of thought and natural language. Cocchiarella’s conceptualist logic also contains an account of the medieval identity (two-name) theory of the copula, as well as an account of plural and mass noun reference and predication, the truth conditions of which are based on a logic of plurals and mass nouns.

Ignacio Angelelli briefly discusses the impact of traditional predication theory on the notion of class. He quotes a text from the 18^th c. by Johann Caspar Sulzer, where not only the notion of class (classis) is used but, moreover, a hierarchy of orders for classes is introduced. Such a hierarchy is developed not along the relation of membership but along the relation of inclusion. Given a class of order n, a class of order n+1 is not one which has the class of order n as a member but one of which the class of order n is a subclass. The main thesis of Angelelli’s paper is that the ordering of classes by inclusion rather than by membership is a consequence of the traditional, as opposed to the Fregean, predication theory.

Allan Bäck looks at the future of predication theory. He observes that in the history of predication, an emphasis has been placed on impersonal statements, a move from speaker meaning to sentence meaning, an elimination of intentionality and standpoint via the elimination of indexicals, and a move from ordinary to ideal language. Following these trends in light of their historical success, Bäck suggests that a theory of predication with the following features should be developed: formalism, having a sharp distinction between the pure theory and its interpretations, and the primacy of two-place relations. Accordingly, he offers a theory of predication with the following features: an uninterpreted language, based on the combinatorials of primitive symbols and on the application of formation rules so as to give well-formed formulae, construction of n-place predicates via unsaturating the wffs, the reduction of all n-place predicates to two-place predicates (relations). Bäck concludes with considering how successfully such a predication theory might be interpreted and applied, in particular to metaphysics.