Peter Simons

λ-calculi are of interest to logicians and computer scientists but have largely escaped philosophical commentary, perhaps because they appear narrowly technical or uncontroversial or both. I argue that even within logic λ-expressions need to be understood correctly, as functors signifying functions in intension within a categorical or typed language. λ-expressions are not names but pure viable binders generating functors, and as such they are of use in giving explicit definitions. But λ is applicable outside logic and computer science, anywhere where the notions of complex whole, substitution, abstraction and structure make sense. To illustrate this, two domains are considered. One is somewhat frivolous: the study of flags; the other is very serious: manufacturing engineering. In each case we can employ λ-abstraction to describe substitutions within a structure, and in the latter case there is even a practical need for such a notation.

It is argued that the source of complexity in language is twofold: repetition, and syntactic embedding. The former enables us to return again and again to the same subject across many sentences, and to maintain the coherence of an argument. The latter is governed by two forms of complexification: the functor-argument structure of all languages and the operator-bound-variable mechanism of familiar formal languages. The former is most transparently represented by categorial grammar, and an extension of this can adequately describe the syntax of variable binders. Both developments have roots within the work of the Lvov-Warsaw School.

In a recent article, Herbert Hochberg portrays my ontological position, that of a trope nominalist who is sceptical about relational tropes, as deviating into idealism. Since there are few philosophical views I find more repugnant than idealism, I must either resist the accusation or recant. I choose to resist, by showing how relational tropes are not needed as truth-makers for a wide range of truths, and raising the real possibility that they may not be needed at all, without lapsing into either monism or idealism

The debate between 3- and 4-dimensionalists is one of the most lively and pervasive in current metaphysics. At stake is a glittering prize: the correct metaphysical analysis of material things and other objects commonly thought to persist in time by enduring. Since we count ourselves among such objects the outcome of the debate is of more than merely academic interest to us. Obviously the ramifications of the debate, even of the points raised by Kit Fine, go far beyond what I can discuss here, so I shall simply select some salient issues and comment on them from my own somewhat heterodox point of view.

I argue that the assumptions that physically basic things are either mereologically atomic, or that they are continuous and there are no atoms, both face difficult conceptual problems. Both views tend to presuppose a largely unquestioned assumption, that things have parts corresponding to the geometric parts of the regions they occupy. To avoid these problems I propose a third view, that physically simple things occupy a finite volume without themselves having parts. This view is examined enough to tease out some of its consequences and show that it withstands the obvious questions it faces. I conclude by mentioning some precedents for this view in Democritus, Kant, and Whitehead, with close variants in Boscovich, Harré, and Markosian.

Commonsense ontology contains both continuants and occurrents, but are continuants necessary? I argue that they are neither occurrents nor easily replaceable by them. The worst problem for continuants is the question in virtue of what a given continuant exists at a given time. For such truthmakers we must have recourse to occurrents, those vital to the continuant at that time. Continuants are, like abstract objects, invariants under equivalences over occurrents. But they are not abstract, and their being invariants enables us to infer both their lack of temporal parts and that non-invariant predications about them must be relativized to times. \\\ [Joseph Melia] In this paper I try to eliminate occurrents from our ontology. I argue against Simons' position that occurrents are needed to supply truthmakers for existential claims about continuants. Nevertheless, those who would eliminate occurrents still need some account of our willingness to assert sentences that logically entail their existence. Though it turns out to be impossible to paraphrase away our reference to occurrents, I show that the truthmakers for such sentences are facts that involve only continuants. This is enough to allow us to regard our ordinary talk about occurrents as fictional. Finally, I argue that a proper conception of the underlying temporal facts about continuants can both avoid the problematic tensed theory of time and the problem of temporary intrinsics.

What primitive concepts does formal ontology require? Forsaking as too indirect the linguistic way of discerning the categories of being, this paper considers what primitives might be required for representing things in themselves (noumena) and representations of them in a thoroughly crafted large autonomous multi-purpose database. Leaving logical concepts and material ontology aside, the resulting 32 categories in 13 families range from the obvious (identity/difference, existence/non-existence) through the fairly obvious (part/whole, one/many, sequential order) and the surprisingly familiar (illocutionary modes, mass/count, indexical/descriptive) to the controversial (moment/fundament, transparent/opaque) and the arcane (modes of class delimitation, taxonomic rank, aspects of designators). Any such list is speculative and tentative, but the test of this one will be in its implementation, a new departure for philosophical category theories.