If structured propositions are logical procedures then how are procedures individuated?

Abstract

This paper deals with two issues. First, it identifies structured propositions with logical procedures. Second, it considers various rigorous definitions of the granularity of procedures, hence also of structured propositions, and comes out in favour of one of them. As for the first point, structured propositions are explicated as algorithmically structured procedures. I show that these procedures are structured wholes that are assigned to expressions as their meanings, and their constituents are subprocedures occurring in executed mode (as opposed to displayed mode). Moreover, procedures are not mere aggregates of their parts; rather, procedural constituents mutually interact. As for the second point, there is no universal criterion of the structural isomorphism of meanings, hence of cohyperintensionality, hence of synonymy for every kind of language. The positive result I present is an ordered set of rigorously defined criteria of fine-grained individuation in terms of the structure of procedures. Hence procedural semantics provides a solution to the problem of the granularity of cohyperintensionality.

Negation and presupposition, truth and falsity

“…24 Note that in this phase C and D are not constituents to be executed; rather they are merely displayed as objects to be selected by the variable c. This is to say that, in TIL, constructions themselves can be objects to be operated on, and without this hyperintensional approach we would not be able to define the strict function if-then-else. For the difference between constructions occurring in the displayed mode (hyperintensionally) and executed mode (as constituents of a super-construction), see, for instance, Duží (2017). 25 The other option would be, for instance, the scenario of talking about those who are asleep, and the sentence would be offered as an answer, "Among those who are asleep are all of John's children".…”

“…Hence, there are no nonexisting individuals.5 Besides, many hold against Russell's translation of atomic sentences like "The F is a G " into the molecular form "There is at least one F and at most one thing is an F and that thing is a G ", because Russell disregards the standard constraint that there must be a fair amount of structural similarity between analysandum and analysans. 6 Nevertheless, for Strawson, sentences are meaningful in and of themselves, independently of empirical facts like the contingent non-existence of the King of France.7 Here I partly draw on and summarise material fromDuží ( , 2014.8 For details on structured meanings, seeJespersen (2012) andDuží (2017).9 For an introduction to the notion of hyperproposition, seeJespersen, (2010) and Jespersen,Duží (2015).10 See, for instance,Hajičová (2008),Gundel (1999),Gundel and Fretheim (2004).…”

Refining Concepts by Machine Learning

“…Since the TIL logical system has been introduced in numerous papers and two books, see, for instance [2,3,4,5,7,8,17], here we just briefly summarise the main principles of a TIL fragment that we need for the purposes of this paper. TIL is a partial, typed hyperintensional lambda calculus with procedural as opposed to settheoretical denotational semantics.…”

“…. 6 For details, see [7]. 7 For the sake of simplicity, here we again use infix notation without Trivialization for the application of the binary relations >, < and the identity = between numbers.…”

“…We call this the task of explicating, or of giving an explication for, the earlier concept [1], (pp. [7][8] Keeping this difference in mind, in this paper we use the term 'refinement' for both cases, including explication of empirical concepts, because in our sample example of explicating the concept of myopia this simplification is harmless.…”