Notion Of Logical Form Research Articles

Numbers, Reference and Russellian Propositions

Stewart Shapiro and John Myhill tried to reproduce some features of the intuitionistic mathematics within certain formal intensional theories of classical mathematics. Basically they introduced a knowledge operator and restricted the ways of referring to numbers and to finite hereditary sets. The restrictions are very interesting, both because they allow us to keep substitutivity of identicals notwithstanding the presence of an epistemic operator and, especially, because such restrictions allow us to see, by contrast, which ways of reference are not compatible with the simultaneous maintenance of substitutivity of identicals and the classical notions of truth and knowledge. In this paper the difference between the restricted and the unrestricted kind of reference is put in relation with Russell's ideas on naming and it is argued that the latter as well is compatible with a certain Russellian conception of the understanding of sentences. Then it is discussed whether and how numbers could be conceived as objects of acquaintance. Finally a general question about the notion of logical form is raised.

‘All A's are B's’: Form and content

This paper argues that universally quantified generalizations have or lack existential import, depending on whether they express lawlike or non-lawlike propositions. This solves the old quarrel between Aristotelian and modern logical analyses of generalizations of this form. But the price we pay is to give up the notion of logical form, since lawlikeness is a question of the epistemic state of the linguistic community, not of form. It is argued that this price is worth paying in any case on independent grounds.

Linguistics and natural logic

Evidence is presented to show that the role of a generative grammar of a natural language is not merely to generate the grammatical sentences of that language, but also to relate them to their logical forms. The notion of logical form is to be made sense of in terms a ‘natural logic’, a logical for natural language, whose goals are to express all concepts capable of being expressed in natural language, to characterize all the valid inferences that can be made in natural language, and to mesh with adequate linguistic descriptions of all natural languages. The latter requirement imposes empirical linguistic constraints on natural logic. A number of examples are discussed.

IV. Davidson's notion of logical form1

IV. Davidson's notion of logical form¹