Henry Laycock

The curiously sweeping assumption that all reference is ‘ultimately’ singular — even in the case of plural or non-count reference — is presented and examined. In the case of plural reference, especially when associated with collective predication, the assumption takes the form of the thought that this is reference to collective entities, plural objects, or sets. Perhaps the most suggestive and profound, albeit notorious idea of this genre is Russell’s doctrine of the ‘class as many’. George Boolos’ explicitly ‘no-class’ approach to the logic of plurality is then compared favourably with ‘reductive’ approaches.

The chapter focuses on quantification as it figures in standard versions of the predicate calculus. These versions are straightforwardly reductive in that non-singular sentences must be re-cast into singular form if they are to receive representation. However, various non-singular sentences, including certain kinds of plural sentences, are refractory to representation in this form. Essentially singular forms of quantifier-expression must be distinguished from non-singular forms to lay the basis for sui generis non-singular forms of quantification, appropriate to both plural nouns and non-count nouns. The maxim ‘to be is to be the value of a variable’ must be rejected.

The notion of an ‘ideal language’ or ‘concept-script’ is explicated and defended, and constraints upon formal systems imposed by the ideal of transparency are explored. It is argued that non-singular symbolisms, including non-singular variables, largely fail to satisfy such constraints. In general, the semantics of non-singular expressions do not transparently reflect the corresponding ontic categories. The conditions for the possibility of transparent non-singular assertions, freed from the concept of identity, are briefly explored. The questionable influence within philosophy of the ‘Classical’ Weltanschaung is highlighted.

The second application of the assumption that singular reference is ‘ultimately’ exhaustive also represents non-count reference as singular — as reference to individual ‘quantities’ or ‘parcels’ of stuff. Unsurprisingly, the idea is sometimes explicitly advanced on the model of plural reference as singular. However, any such view must attempt to circumvent the difficulties posed by Russell’s analysis of the conditions, whereby descriptions count as semantically singular. It is argued that such an attempt cannot succeed.

This chapter takes issue with the common assumption that referential expressions and definite descriptions involving ‘mass nouns’ are semantically singular, thereby designating so-called parcels of matter or individual instances of stuff. The trouble is that whereas count nouns are either singular or plural, the so-called mass nouns, because they are non-count, are semantically neither singular nor plural. Russell’s Theory of Descriptions as well as considerations on persistence, identity, and flux are invoked to reinforce this point.

My objective is a better comprehension of two theoretically fundamental concepts. One, the concept of a substance in an ordinary (non-Aristotelian) sense, ranging over such things as salt, carbon, copper, iron, water, and methane – kinds of stuff that now count as (chemical) elements and compounds. The other I’ll call the object-concept in the abstract sense of    Russell, Wittgenstein, and Frege in their logico-semantical enquiries. The material object-concept constitutes the heart of our received logico / ontic system, still massively influenced by Aristotle after almost 2.5 millennia. On such an account, the fundamentality of material objects and their attributes are the metaphysical basis of the cosmos, as reflected in our received logic, Quine’s ‘canonical notation’ – derived via the empiricism of Russell from Frege’s function-based Begriffschrifft, and consisting of concrete singular terms and variables, quantifiers and predicate-expressions. The inadequacy of Frege’s approach to understanding concepts is reflected in his initial question. Frege enquires of ‘what it is that we are calling an object’, remarking that he regards a regular definition as impossible: “we have here something too simple to admit of logical analysis”. The imagined ultimacy or simplicity of the idea of a single object (arithmetically, just a unit – one as against two, three, four, etc.) as foundational to the calculus is just that – imagined. It is also guaranteed to block the comprehension of the substance-concept.

Mereological entities often seem to violate ‘ordinary’ ideas of what a concrete object can be like, behaving more like sets than like Aristotelian substances. However, the mereological notions of ‘part’, ‘composition’, and ‘sum’ or ‘fusion’ appear to find concrete realisation in the actual semantics of mass nouns. Quine notes that ‘any sum of parts which are water is water’; and the wine from a single barrel can be distributed around the globe without affecting its identity. Is there here, as some have claimed, a ‘natural’ or ‘innocent’ form of mereology? The claim rests on the assumption that what a mass noun such as ‘wine’ denotes — the wine from a single barrel, for example — is indeed a unit of a special type, the sum or fusion of its many ‘parts’. The assumption is, however, open to question on semantic grounds.

Resolution of the problem of mass nouns depends on an expansion of our semantic/ontological taxonomy. Semantically, mass nouns are neither singular nor plural; they apply to neither just one object, nor to many objects, at a time. But their deepest kinship links them to the plural. A plural phrase — 'the cats in Kingston' — does not denote a single plural thing, but merely many distinct things. Just so, 'the water in the lake' does not denote a single aggregate — it is not ONE, but rather MUCH. The world is not the totality of singular objects, plural objects, and mass objects; for there are no plural or mass objects. It is the totality of single objects and (just) stuff.

Mills writes: G. A. Cohen's influential ‘technological determinist’ reading of Marx's theory of history rests in part on an interpretation of Marx's use of ‘material’ whose idiosyncrasy has been insufficiently noticed. Cohen takes historical materialism to be asserting the determination of the social by the material/asocial, viz. ‘socio‐neutral’ facts about human nature and human rationality which manifest themselves in a historical tendency for the forces of production to develop. This paper reviews Marx's writings to demonstrate the extensive textual evidence in favour of the traditional interpretation ‐ that for Marx, the ‘material’ includes the economic, and is thus ineluctably social in character. Thus those critics of Cohen who have urged the inclusion of the relations of production in historical materialism's explanans do seem to have Marx's terminological and conceptual backing.

The theory of surplus value contrasts ‘pay for labour power’ and ‘pay for labour services’. Unlike labour services but like all commodities, labour power has a specific economic value and it exchanges at this value. Unlike that of other commodities, the consumption of labour power results in the creation of more value than the commodity itself contains. Surplus value arises from the gap between the labour needed to sustain a day’s work, to keep the worker going for a day, and the labour performed in that same time. By the labour theory of value, the amount of labour needed to sustain a day’s work confers one value on the means of subsistence the worker requires, and thereby on the labour power the worker sells to her employer, whereas the day’s work itself confers another larger value on the product marketed by the employer.

"Matter" may be defined, according to the Oxford English Dictionary, as "The substance, or the substances collectively, out of which a physical object is made or of which it consists". And while the O.E.D. is not the ultimate authority on words, nor is it, I believe, far wrong in this particular case. The definition is, as I shall argue in this paper, in substantial harmony with a tradition of some antiquity, according to which material objects do not constitute a somehow 'fundamental category' for ontology; and it is in conflict with a more contemporary view which maintains precisely that they do.