Transparent quantification into hyperpropositional contexts de re

This paper is the twin of (Duží and Jespersen, in submission), which provides a logical rule for transparent quantification into hyperprop- ositional contexts de dicto, as in: Mary believes that the Evening Star is a planet; therefore, there is a concept c such that Mary be- lieves that what c conceptualizes is a planet. Here we provide two logical rules for transparent quantification into hyperpropositional contexts de re. (As a by-product, we also offer rules for possible- world propositional contexts.) One rule validates this inference: Mary believes of the Evening Star that it is a planet; therefore, there is an x such that Mary believes of x that it is a planet. The other rule validates this inference: the Evening Star is such that it is believed by Mary to be a planet; therefore, there is an x such that x is believed by Mary to be a planet. Issues unique to the de re variant include partiality and existential presupposition, sub- stitutivity of co-referential (as opposed to co-denoting or synony- mous) terms, anaphora, and active vs. passive voice. The validity of quantifying-in presupposes an extensional logic of hyperinten- sions preserving transparency and compositionality in hyperinten- sional contexts. This requires raising the bar for what qualifies as co-denotation or equivalence in extensional contexts. Our logic is Tichý’s Transparent Intensional Logic. The syntax of TIL is the typed lambda calculus; its highly expressive semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The two non-standard features we need are a hyper- intension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hy- perintensions

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

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 sub-procedures 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 co-hyperintensionality, 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 co-hyperintensionality

Concepts as hyperintensional objects

The author defends the view that the notion of concept, if used in the logical (not cognitivist) tradition, should be explicated procedurally (i.e., not set-theoretically). He argues that Tichý’s Transparent Intensional Logic is an apt tool for such an explication and derives the respective definition. Some consequences of this definition concern the notions of emptiness, simple concepts, empirical concepts and algorithmic concepts

Towards an extensional calculus of hyperintensions

In this paper I describe an extensional logic of hyperintensions, viz. Tichý's Transparent Intensional Logic (TIL). TIL preserves transparency and compositionality in all kinds of context, and validates quantifying into all contexts, including intensional and hyperintensional ones. The received view is that an intensional (let alone hyperintensional) context is one that fails to validate transparency, compositionality, and quantifying-in; and vice versa, if a context fails to validate these extensional principles, then the context is 'opaque', that is non-extensional. We steer clear of this circle by defining extensionality for hyperintensions presenting functions, functions (including possible-world intensions), and functional values. The main features of our logic are that the senses of expressions remain invariant across contexts and that our ramified type theory enables quantification over any logical objects of any order into any context. The syntax of TIL is the typed lambda calculus; its semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The only two non-standard features of our logic are a hyperintension called Trivialization and a fourplace substitution function (called Sub) defined over hyperintensions. Using this logical machinery I propose rules of existential generalization and substitution of identicals into the three kinds of context.Web of Science191452

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

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 sub-procedures 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 co-hyperintensionality, 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 co-hyperintensionality

Deduction in TIL: from simple to ramified hierarchy of types

Tichý’s Transparent Intensional Logic (TIL) is an overarching logical framework apt for the analysis of all sorts of discourse, whether colloquial, scientific, mathematical or logical. The theory is a procedural (as opposed to denotational) one, according to which the meaning of an expression is an abstract, extra-linguistic procedure detailing what operations to apply to what procedural constituents to arrive at the product (if any) of the procedure that is the object denoted by the expression. Such procedures are rigorously defined as TIL constructions. Though TIL analytical potential is very large, deduction in TIL has been rather neglected. Tichý defined a sequent calculus for pre-1988 TIL, that is TIL based on the simple theory of types. Since then no other attempt to define a proof calculus for TIL has been presented. The goal of this paper is to propose a generalization and adjustment of Tichý’s calculus to TIL 2010. First I briefly recapitulate the rules of simple-typed calculus as presented by Tichý. Then I propose the adjustments of the calculus so that it be applicable to hyperintensions within the ramified hierarchy of types. TIL operates with a single procedural semantics for all kinds of logical-semantic context, be it extensional, intensional or hyperintensional. I show that operating in a hyperintensional context is far from being technically trivial. Yet it is feasible. To this end we introduce a substitution method that operates on hyperintensions. It makes use of a four-place substitution function (called Sub) defined over hyperintensions.Web of Science20suppl 236

Communication in a multi-cultural world

The goal of this paper is to demonstrate that procedurally structured con- cepts are central to human communication in all cultures and throughout history. This thesis is supported by an analytical survey of three very different means of communication, namely Egyptian hieroglyphs, pictures, and Inca knot writing known as khipu. My thesis is that we learn, communicate and think by means of concepts; and regardless of the way in which the meaning of an expression is encoded, the meaning is a concept. Yet we do not define concepts within the classical set-theoretical framework. Instead, within the logical framework of Transparent Intensional Logic, we explicate concepts as logical procedures that can be assigned to expressions as their context-invariant meaning. In particular, complex meanings, which structurally match complex expressions, are complex procedures whose parts are sub-procedures. The moral suggested by the paper is this. Concepts are not flat sets; rather, they are algorithmically structured abstract procedures. Unlike sets, concepts have constituent sub-procedures that can be executed in order to arrive at the product of the procedure (if any). Not only particular parts matter, but also the way of combining these parts into one whole ‘instruction’ that can be followed, understood, executed, learnt, etc., matters.Web of Science21221819