Abstract for ”Talking about Properties”

 

My paper is an enquiry into the semantic relations between general terms and (canonical) designators of properties.

In part one of my paper I examine the semantic profile of canonical designators of properties, like ”redness” and ”the property of being red”. In part two I discuss the meaning of whole sentences in which such designators occur,  namely explicit property-ascriptions like ”a possesses F-ness”.

My main contention is that designators of properties express complex concepts which can be analysed in recourse to concepts expressed by corresponding general terms. To use a slogan, I content that general terms do not refer to properties at all, but that, at the same time, they provide the conceptual basis of the framework of properties employed in ordinary language (I shall not come back to the slogan in this abstract but rather stick to the details of my account).

 

 

I. Canonical Designators of Properties

 

(a. Canonical Designators)

I begin with a short taxonomy of singular terms for properties. I distinguish two kinds of canonical designators: firstly there are fully-fledged substantives like wisdom”, ”redness” etc. (in what follows I shall call them terms of Class I) and secondly there are gerundive constructions of the form ”the property (or: quality) of being F” (terms of Class II).

 

(b. Designators of the form ”the property of being F”)

Then I turn to the question about how to classify terms of Class II in light of the common division of singular terms into definite descriptions and proper names. Though terms of Class II may at first, due to the occurrence of the definite article, look like descriptions, it turns out that they resist an analysis in a classical Russellian manner. Take the standard condition:

(RD)    For all x:    ”the j” denotes x « (i) x is a j & (ii) apart from x there is no other j.

To apply this to a term ”the j”, the contained ”j” should behave as a count noun (since it must combine with an indefinite article in (RD)). However, ”property of being F” does not fulfil this requirement; the relevant instance of (RD) seems to be rather nonsensical:

(RD*)  For all x:    ”the property of being F” denotes x « (i) x is a property of being F &

                                                                       (ii) apart from x there is no other property of being F.

I suggest to regard ”the property of being F” as an appositive description, comparable to ”the number 7” or ”the name ‘John’”. It consists of two parts: (i) a juxtaposed singular term (”being F”) which is coreferential with the whole expression and (ii) an appositive term (”property”) that is true of the object denoted by the singular term.

I show how to treat appositive descriptions along an expansion of the Russellian account. The idea is to break up the appositive description (of the form ”the j a”) into its two components and provide them with an individual treatment. While the appositive part easily fits the scheme of (RD), the trick of incorporating the problematic part ”a” consists in building a predicate from it by adding the sign of identity. Thus we get the following scheme:

(RAD) For all x:    ”the j a” denotes x « (i) x is a j & (ii) x = a.

On the basis of this discussion we can say that terms of Class II really are definite descriptions – appositive ones. But now a new question arises: what is the status of the gerundive part of ”the property of being F”?

 

(c. Designators of the form ”being F”)

The gerundive ”being F” cannot be classified as a definite description. It does contain descriptive parts whose meaning is relevant to the meaning of the term, but the descriptive material is not true of the property denoted – the property of being verbose is surely not itself verbose (rather it is true of those things which have the denoted property).

At the same time these terms bear distinctive marks which proper names typically lack:

(i)    their conditions of understanding are systematically dependent upon the conditions of understanding their components,

(ii)   their reference is a function of their meaning,

(iii)   knowing their meaning suffices for knowing their reference.

Because of these features, gerundive property designators are not proper names; since they are not definite descriptions either, we should accept the existence of another class of singular terms. I finally argue that the results are equally valid for Class I terms. Thus, canonical property terms have a very peculiar semantic shape (while a Class II term can at least be counted as an appositive descriptions, its ”heart” cannot).

 

 

II. Property Ascriptions and Simple Predications

 

(a. Against the Synonymy Thesis)

Here I discuss the semantic relations between simple predications of the form

(SP)     a is F,

and explicit property-ascriptions of the form

(EP)     a has the property of being F (or: F-ness).

Now it is a widespread and apparently very plausible thesis, unanimously held by philosophical antagonists as Strawson and Quine, [1]  that corresponding statements of these forms are nothing but stylistic variants of each

 

other (that is, they are synonymous in the strictest sense of the word). Call this the Synonymy Thesis – I shall argue against it.

My main argument is the following:

(P1)     Simple predications and corresponding property-ascriptions differ in their conditions of understanding.

(P2)     If two statements differ in their conditions of understanding, then they express different propositions and accordingly they are not synonymous.

(C)       A simple predication is not synonymous with the corresponding property-ascription.

I go on to argue for the crucial premise of the argument, (P1). Since designators of properties are such that knowledge of their meaning suffices for knowledge of their referent, whoever understands a property-ascription must possess knowledge about properties. Since no such knowledge is required for understanding simple predications, (P1) is warranted.

 

How exactly does one acquire knowledge about properties then? One has to adopt the conceptual framework of properties, and this is essentially done by learning a fragment of English which explicitly deals with properties:

(F-1) one has to learn how to generate designators of properties and the bilaterally inferential relation between simple predications and corresponding property-ascriptions.

(F-2) one has to learn to use designators of properties as singular terms; that is, one must allow oneself to quantification into their position and to use higher-level predication.

My position would not be complete if I could not provide a positive account of the obviously very close semantic relation between a simple predication and the corresponding property-ascription. But I can: The concept expressed by a canonical designator of a property can be analysed with recourse to the concept expressed by the correlated general term. As an example take the following analysis of the concept expressed by ”wisdom”:

(PA)  x = wisdom «_Df.   x is the property which, of necessity, all and only those entities which are wise have in common.

Of course, by this analysis I have not explained what it is to be wise – my goal was much more modest. I explained what a certain property, namely wisdom, is and I relied on an understanding of the general term ”wise”. With this analysis I can explain the semantic relation between a simple predication and a property-ascription. The latter contains a conceptually complex component which allows for an analysis in terms of a component of the first, such that the truth of the property-ascription is grounded in the truth of the simple predication.

 

(b. Virtual and Real Property Discourse)

In the last section of my paper I try to calm those who side with Quine and Strawson in accepting the Synonymy Thesis and I offer an addition to my position which may allow them to meet me halfway. For this I make use of Quine’s idea of Virtual Set Theory (VST) This theory comprises linguistic forms which we also meet in standard set theory. However, these forms are introduced as mere notational variants of certain simple predications. Thus, by definition,

Socrates Î {x: x is wise}

says literally the same as

Socrates is wise.

The point of VST is that we can simulate set theory without talking about sets at all. But the simulative powers of VST are limited: not every significant statement of real set theory has a correspondence in VST.

I use Quine’s idea to draw a certain picture of property talk. We can make sense of Virtual Property Talk (VPT) in which statements that apparently deal with properties are introduced as mere synonyms for simple predications. But just as VST does not really talk about sets at all, VPT does not really talk about properties.

However, we may regard VPT as important for learning genuine property talk. We may learn to use property-ascriptions as mere stylistic variants of simple predications (just as the process of learning set theory may start with the adoption of VST). But as long as we do this, we do not treat designators of properties as singular terms. The crucial step from VPT to genuine property talk consists in allowing linguistic forms (see (F-2) above) that do not allow for strict translations into simple predications.

The analogy (of which I could give only a rough sketch in this abstract) should account for the intuition (to which Strawson and Quine gave voice) that the synonymy of simple predications and property-ascriptions is quite evident (such that its denial is even absurd) – for I may agree that the latter have one use in which they are synonymous with the former. It is their use as part of VPT which may be seen as forming a part of our language – property-ascriptions, on my view, then have two readings, a ”virtual” and a ”genuine” one.