As we have seen (read the previous post here), predicates such as be red, be sleeping, snores, be a horse etc. may be conceived of as functions from individuals in truth values. What about more complex predicates as those which turn up in the following sentences: John loves Mary, Peter is bigger than Chris, John gives money to the poor, Mary put the necklace around her neck etc.? These are clearly predicates which define a relation between two or three individuals, hence 2- or 3-place-predicates. There are several ways to deal with them. The preferable way seems to be to consider them as “stacked” 1-place-predicates. This is a property of human languages not shared by any known other system of communication. (An exception may be the structure of DNA.) We say that human language is “recursive”. That means that we may apply an operation to its own output, thus (in principle) to infinity. This is the core property of the syntax of human languages, and it mirrors in a way the semantic structure of complex predicates. Thus syntax is a (mental) structure of the combination of words. From this structure, the semantics of a complex utterance can be computed. This is called the principle of compositionality, which was assumed by Frege: The meaning of complex forms derives from the meanings of its simple parts and the manner of their composition.

In this respect, a complex predicate like”(John) loves (Mary)” may be structured as followed: There is a 1-place predicate of the form LOVE (Mary) which in itself is a 1-place predicate for the subject, John: [[ LOVE (Mary)] ( John) ]. The most deeply embedded predicate [ LOVE (y)] is true for all individuals (y) which are being loved (by someone), and [[ LOVE (Mary) ] (x) ] is the set of all individuals (x) which have the property of loving Mary.

In a similar vein, a 3-place-predicate like John gives money to the poor may be decomposed into something like [[[ GIVE (money)] (to the poor)] (John) ].

Note that this decomposition reflects the fact that GIVE is a predicate which consists of a basic state (John owns or possesses the money), a change of this state, i.e. a process (later on, the poor will possess the money) and someone who Causes this process, namely John. You may look this up in an earlier post of mine called “What do we talk about?”.

Completely in the vein of compositionality, the internal semantic structure of these predicates is reflected in the syntactic structure in which they occur. This is in fact true of most linguistic expressions, but there are some complications and (apparent) deviations – otherwise linguists wouldn’t have much to work on. A very prominent example is given in the apparently similar sentences

John is easy to please. (It is easy (for someone) to please John)

John is eager to please. (John is eager to please someone).

It is with these cases and others that the so-called transformational grammar is concerned.

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Prof. Dr. Jürgen Lenerz, born 1945, was a professor for German Linguistics at the University of Cologne from 1985 until his retirement in 2011. His main interests are in the interaction of syntax, semantics, intonation and information structure in natural languages

When asked what we talk about, we would possibly say that we talk about “the world”. But what is the world? Perhaps we would say that the world somehow exists outside of ourselves (including ourselves) and consists of a huge number of interrelated situations, where the interrelations are due to the laws of physics, of social behavior etc. This is what we sometimes call the “real” world. But mind you that the only evidence we have about the “existence” of the real world is our mental representation of this world. So, in a different sense, the world of our knowledge of the real word is another “real” world in our mind. This is so because our mind is the most real thing we may think of (recall Descartes). Our knowledge of the world arises from various sensual experiences from “without”, as it were, and from hearsay about the world, i.e. from what others tell us about the world.

Knowledge (of the world) is in part propositional, in part it is not propositional. What does that mean? A proposition is the meaning of a statement about (a situation in) the world. If Leo is a horse, then the statement Leo is a horse is true with respect to that situation. The meaning of this statement (regardless of its truth) may be paraphrased as that Leo is a horse or as whether Leo is a horse (or not). This is what we mean by the technical term “proposition”, and part of our knowledge may be expressed in such propositions. This is what we can talk about.

What we cannot talk about is our non-propositional knowledge.  So, Balotelli “knows” how to kick the ball into the goal without being able to explain this in any way in a number of propositions. It is somehow “tacit knowledge”, and much of what we “know” is of such kind: we know what it feels like to be kissed or we know how coffee smells etc. So, this part of our knowledge is not part of what we call “semantics”. Semantics is concerned only with propositional meaning.

Talking to each other will add to (or revise) our propositional knowledge of the world. So, the “world” is somehow the set of propositions we consider as true with respect to the world.

How many worlds are there? Infinitely many! Normally, we don’t talk about the “real” world but about hypothetical worlds ( If Sarkozy had won the latest elections, then… ) or about a world we wish to be ( Had I but kissed the girl. May he live forever! ) or a world of fiction (take any example from the vast realm of novels) or any number of other worlds. All these worlds are, of course, worlds of our imaginations, but the point is that they are “real” worlds in our minds. All these worlds are “possible worlds”, and this is why modern logical semantics is often called a “possible world semantics”. Possible worlds are described by the set of propositions which are true of these worlds. Propositions which are true of a possible world are called “statements” about this world.

When talking to each other, we talk about our joint “discourse world”.

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Prof. Dr. Jürgen Lenerz, born 1945, was a professor for German Linguistics at the University of Cologne from 1985 until his retirement in 2011. His main interests are in the interaction of syntax, semantics, intonation and information structure in natural languages