We present here the papers selected for the volume on the Unity of Propositions problems. After summarizing what the problems are, we locate them in a spectrum from those aiming to provide substantive, reductive explanations, to those with a more deflationary take on the problems.

This paper addresses the mereological problem of the unity of structured propositions. The problem is how to make multiple parts interact such that they form a whole that is ultimately related to truth and falsity. The solution I propose is based on a Platonist variant of procedural semantics. I think of procedures as abstract entities that detail a logical path from input to output. Procedures are modeled on a function/argument logic, but are not functions. Instead they are higher-order, fine-grained structures. (...) I identify propositions with particular kinds of molecular procedures containing multiple sub-procedures as parts. Procedures are among the basic entities of my ontology, while propositions are derived entities. The core of a structured proposition is the procedure of predication, which is an instance of the procedure of functional application. The main thesis I defend is that procedurally conceived propositions are their own unifiers detailing how their parts interact so as to form a unit. They are not unified by one of their constituents, e.g., a relation or a sub-procedure, on pain of regress. The relevant procedural semantics is Transparent Intensional Logic, a hyperintensional, typed λ-calculus, whose λ-terms express four different kinds of procedures. While demonstrating how the theory works, I place my solution in a wider historical and systematic context. (shrink)

We demonstrate how to validly quantify into hyperintensional contexts involving non-propositional attitudes like seeking, solving, calculating, worshipping, and wanting to become. We describe and apply a typed extensional logic of hyperintensions that preserves compositionality of meaning, referential transparency and substitutivity of identicals also in hyperintensional attitude contexts. We specify and prove rules for quantifying into hyperintensional contexts. These rules presuppose a rigorous method for substituting variables into hyperintensional contexts, and the method will be described. We prove the following. First, it (...) is always valid to quantify into hyperintensional attitude contexts and over hyperintensional entities. Second, factive empirical attitudes validate, furthermore, quantifying over intensions and extensions, and so do non-factive attitudes, both empirical and non-empirical , provided the entity to be quantified over exists. We focus mainly on mathematical attitudes, because they are uncontroversially hyperintensional. (shrink)

Logical semantics includes once again structured meanings in its repertoire. The leading idea is that semantic and syntactic structure are more or less isomorphic. A key motive for reintroducing sensitivity to semantic structure is to obtain fine‐grained meanings, which are individuated more finely than in possible‐world semantics, namely up to necessary equivalence. Just getting the truth‐conditions right is deemed insufficient for a full semantic analysis of sentences. This paper surveys some of the most recent contributions to the program of structured (...) meaning, while providing historical background. I suggest that to make substantial advances the program needs to solve the problem of propositional unity and develop an intensional mereology of abstract objects. (shrink)

The topic of this special issue of Synthese is hyperintensionality. This introduction offers a brief survey of the very notion of hyperintensionality followed by a summary of each of the papers in this collection. The papers are foundational studies of hyperintensionality accompanied by ample philosophical applications.Hyperintensionality concerns the individuation of non-extensional entities such as propositions and properties, relations-in-intension and individual roles, as well as, for instance, proofs and judgments and computational procedures, in case these do not reduce to any of (...) the former. Hyperintensional individuation is frequently also referred to as ‘fine-grained’ or sometimes simply ‘intensional’ individuation, when ‘intensional’ is not understood in the specific sense of possible-world semantics or in the pejorative sense of flouting various logical rules of extensional logic. A principle of individuation qualifies as hyperintensional as soon as it is finer than necessary .. (shrink)

Aim of the paper is to present a new logic of technical malfunction. The need for this logic is motivated by a simple-sounding philosophical question: Is a malfunctioning corkscrew, which fails to uncork bottles, nonetheless a corkscrew? Or in general terms, is a malfunctioning F, which fails to do what Fs do, nonetheless an F? We argue that ‘malfunctioning’ denotes the modifier Malfunctioning rather than a property, and that the answer depends on whether Malfunctioning is subsective or privative. If subsective, (...) a malfunctioning F is an F; if privative, a malfunctioning F is not an F. An intensional logic is required to raise and answer the question, because modifiers operate directly on properties and not on sets or individuals. This new logic provides the formal tools to reason about technical malfunction by means of a logical analysis of the sentence “a is a malfunctioning F”. (shrink)

Theories of structured meanings are designed to generate fine-grained meanings, but they are also liable to overgenerate structures, thus drawing structural distinctions without a semantic difference. I recommend the proliferation of very fine-grained structures, so that we are able to draw any semantic distinctions we think we might need. But, in order to contain overgeneration, I argue we should insert some degree of individuation between logical equivalence and structural identity based on structural isomorphism. The idea amounts to forming an equivalence (...) class of different structures according to one or more formal criteria and designating a privileged element as a representative of all the elements, i.e., a first among equals. The proposed method helps us to a cluster of notions of co-hyperintensionality. As a test case, I consider a recent objection levelled against the act theory of structured propositions. I also respond to an objection against my methodology. (shrink)

The topic of this paper is the notion of technical (as opposed to biological) malfunction. It is shown how to form the property being a malfunctioning F from the property F and the property modifier malfunctioning (a mapping taking a property to a property). We present two interpretations of malfunctioning. Both interpretations agree that a malfunctioning F lacks the dispositional property of functioning as an F. However, its subsective interpretation entails that malfunctioning Fs are Fs, whereas its privative interpretation entails (...) that malfunctioning Fs are not Fs. We chart various of their respective logical consequences and discuss some of the philosophical implications of both interpretations. (shrink)

Soames's cognitive propositions are strings of acts to be performed by an agent, such as predicating a property of an individual. King takes these structured propositions to task for proliferating too easily. King's objection is based on an example that purports to show that three of Soames's propositions are really just one proposition. I translate the informally stated propositions King attributes to Soames into the intensional λ-calculus. It turns out that they are all β-equivalent to the proposition King claims Soames's (...) three propositions are identical to. I argue on philosophical grounds against identifying β-equivalent propositions. The reason is that β-conversion obliterates too many of the procedural distinctions that are central to an act-based theory such as Soames's and which are worth preserving. In fact, β-expansion allows the addition of a fifth proposition that highlights additional procedural distinctions and propositional structure. The welcome conclusion is that we have five procedurally distinct, if equivalent, propositions. (shrink)

In his 2000 book Logical Properties Colin McGinn argues that predicates denote properties rather than sets or individuals. I support the thesis, but show that it is vulnerable to a type-incongruity objection, if properties are (modelled as) functions, unless a device for extensionalizing properties is added. Alternatively, properties may be construed as primitive intensional entities, as in George Bealer. However, I object to Bealer’s construal of predication as a primitive operation inputting two primitive entities and outputting a third primitive entity. (...) Instead I recommend we follow Pavel Tichý in construing both predication and extensionalization as instances of the primitive operation of functional application. (shrink)

The purpose of this article is to provide a non‐contradictory interpretation of sentences such as “Smith's murderer might not have murdered Smith”. An anti‐actualist, two‐dimensional framework including partial functions provides the basis for my solution. I argue for two claims. The modal profile of the proposition expressed by “The F might not have been an F” is complex: at any world where there is a unique F the proposition is true; at any world without a unique F the proposition has (...) no truth‐value; hence, at no world is it false. It remains an open semantic and epistemological question which of the first two kinds of world the actual world is. The semantic method should be based on explicit intensionalization in lieu of actualism. Actualism accords a privileged role to the actual world. Explicit intensionalization places all possible worlds, including the actual one, on an equal footing. Syntactically, a lambda‐bound world variable replaces the actual‐world constant or operator, while the other world variable is existentially bound. (shrink)

We prove how to validly quantify into hyperpropositional contexts de dicto in Transparent Intensional Logic. Hyperpropositions are sentential meanings and attitude complements individuated more finely than up to logical equivalence. A hyperpropositional context de dicto is a context in which only co-hyperintensional propositions can be validly substituted. A de dicto attitude ascription is one that preserves the attributee’s perspective when one complement is substituted for another. Being an extensional logic of hyperintensions, Transparent Intensional Logic validates all the rules of extensional (...) logic, including existential quantification. Yet the rules become more exacting when applied to hyperintensional contexts. The rules apply to only some types of entities, because the existence of only some types of entities is entailed by a hyperpropositional attitude de dicto. The insight that the paper offers is how a particular logic of hyperintensions is capable of validating quantifying-in in a principled and rigorous manner. This result advances the community-wide understanding of how to logically manipulate hyperintensions. (shrink)

The standard rule of single privative modification replaces privative modifiers by Boolean negation. This rule is valid, for sure, but also simplistic. If an individual a instantiates the privatively modified property (MF) then it is true that a instantiates the property of not being an F, but the rule fails to express the fact that the properties (MF) and F have something in common. We replace Boolean negation by property negation, enabling us to operate on contrary rather than contradictory properties. (...) To this end, we apply our theory of intensional essentialism, which operates on properties (intensions) rather than their extensions. We argue that each property F is necessarily associated with an essence, which is the set of the so-called requisites of F that jointly define F. Privation deprives F of some but not all of its requisites, replacing them by their contradictories. We show that properties formed from iterated privatives, such as being an imaginary fake banknote, give rise to a trifurcation of cases between returning to the original root property or to a property contrary to it or being semantically undecidable for want of further information. In order to determine which of the three forks the bearers of particular instances of multiply modified properties land upon we must examine the requisites, both of unmodified and modified properties. Requisites underpin our presuppositional theory of positive predication. Whereas privation is about being deprived of certain properties, the assignment of requisites to properties makes positive predication possible, which is the predication of properties the bearers must have because they have a certain property formed by means of privation. (shrink)

In a 2010 paper Daley argues, contra Fodor, that several syntactically simple predicates express structured concepts. Daley develops his theory of structured concepts within Tichý’s Transparent Intensional Logic . I rectify various misconceptions of Daley’s concerning TIL. I then develop within TIL an improved theory of how structured concepts are structured and how syntactically simple predicates are related to structured concepts.

Circumstantialists already have a logical semantics for impossibilities. They expand their logical space of possible worlds by adding impossible worlds. These are impossible circumstances serving as indices of evaluation, at which impossibilities are true. A variant of circumstantialism, namely modal Meinongianism (noneism), adds impossible objects as well. These are so-called incomplete objects that are necessarily non-existent. The opposite of circumstantialism, namely structuralism, has some catching-up to do. What might a structuralist logical semantics for impossibilities without impossibilia look like? This paper (...) makes a structuralist counterproposal. We present a semantics based on a procedural interpretation of the typed λ-calculus. The fundamental idea is that talk about impossibilities should be construed in terms of procedures: some yield as their product a condition that could not possibly have a satisfier, while the rest fail to yield a product altogether. Dispensing with a ‘bottom’ of impossibilia requires instead a ‘top’ consisting of structured hyperintensions, intensions, intensions defining other intensions, a typed universe, and dual (de dicto and de re) predication. We explain how the theory works by going through several examples. (shrink)

This paper defendsintensional essentialism: a property (intensional entity) is not essential relative to an individual (extensional entity), but relative to other properties (or intensional entities). Consequently, an individual can have a property only accidentally, but in virtue of having that property the individual has of necessity other properties. Intensional essentialism is opposed to various aspects of the Kripkean notion of metaphysical modality, eg, varying domains, existence as a property of individuals, and its category of properties which are both empirical and (...) essential with respect to particular individuals and natural kinds. The key notion of intensional essentialism isrequisite. A requisite is explicated as a relation-in-extension between two intensions (functions from possible worlds and moments of time)X, Y such that wherever and wheneverX is instantiatedY is also instantiated. We predict three readings of the sentence. Every wooden table is necessarily wooden , one involving modalityde re and the other two modalityde dicto. The first reading claims that no individual which is a wooden table is necessarily wooden. The claim is backed up by bare particular anti-essentialism. The two other interpretations claim that it is necessary that whatever is a wooden table is wooden. However, as we try to show, one is logically far more perspicuous thanks to the concept of requisite and thus preferable to more standardde dicto formalizations. (shrink)

I offer a two-tiered critique of epistemological contrastivism as developed by Jonathan Schaffer. First, I investigate the cornerstone of contrastivism, the notion of knowing the selected proposition p rather than the eliminated, or contrast, proposition q. Contrastivism imposes the ternicity constraint that the knowledge relation should span a knower and two propositions. However, contrastivism has yet to explain how to square this constraint with the required contrast between the selected and the eliminated propositions, and it is not immediately obvious how (...) to accomplish this. I offer up for consideration the binary proposal that to know that p rather than q is to know that the conjunction of p and the negation of q is true. Second, I argue that contrastivist objects of knowledge ought to be hyperpropositions rather than functions from possible worlds to truth-values, as assumed by Schaffer. (shrink)

In a 1997 paper Jennifer Saul adduces various examples of simple sentences in which the substitution of one co-referential singular term for another appears to be invalid. I address the question of whether anti-substitution is logically justified by examining the validity and soundness of substitution of co-referential singular terms in three simple-sentence arguments each exhibiting a different logical structure. The result is twofold. First, all three arguments are valid, provided Leibniz’s Law is valid with respect to simple sentences . Thus, (...) as far as these arguments are concerned, there is no logical problem with substitution in simple sentences. Second, two of the arguments cannot be sound, because their respective sets of premises are inconsistent. Thus, it would be logically irrational to commit oneself to all the premises of the respective arguments. To the extent that the origin of Saul’s puzzles is in logic , I suggest, tentatively, that substitution may appear to be invalid because the issues of validity and soundness have not been kept separate. I then consider in depth Saul’s first sentence, “Clark Kent enters a phone booth and Superman exits”. Obviously, two-way substitution is trivially valid, if the expressions are co-referential semantically proper names, the conclusion being but a rephrasing of the premise. However, I argue that a non-trivial semantic analysis of this sentence should take account of the diachronicity of Clark Kent’s entrance and Superman’s exit while preserving the internal link between being Superman and being Clark Kent. I propose the following. ‘Superman’ and ‘Clark Kent’ refer to two distinct individual concepts. “Superman is Clark Kent” then no longer expresses the self-identity of an individual bearing two names, but that two named concepts are held together by the requisite relation: wherever and whenever someone falls under the concept of Superman the same individual also falls under the Clark Kent concept, whereas there are exceptions to the converse. This semantic analysis always validates the substitution of ‘Clark Kent’ for ‘Superman’, but validates the substitution of ‘Superman’ for ‘Clark Kent’ only if the additional condition is met that somebody should fall under the Superman concept when Clark Kent. (shrink)

In a 2005 paper Ólafur Páll Jónsson presents a puzzle that turns on intentional identity and definite descriptions. He considers eight solutions and rejects them all, thus leaving the puzzle unsolved. In this paper I put forward a solution. The puzzle is this. Little Lotta wants most of all a bicycle for her birthday, but she gets none. Distracted by the gifts she does receive, she at first does not think about the bike. But when seeing her tricycle, she is (...) reminded of the bike. The question is how we are to analyse these two occurrences of ‘the bike’ in the absence of a unique bike that Lotta wants. So the semantics of ‘the bike’ needs to be spelt out, and it must be made explicit what the complements of Lotta’s attitudes are. My analysis shows that the attributer’s usage of ‘the bike’ blurs the distinction between a second-order and a first-order intension (a property concept and a property, respectively). My solution can be summed up in this two-premise argument. (a) In the state-of-affairs S, the property of being a bike is the extension of the property concept the property such that Lotta wants an instance of it more than any other; (b) in S, Lotta does not think about/is reminded of the property that she wants an instance of more than any other; (c) therefore, in S Lotta does not think about/is reminded of the property of being a bike. This solution requires looking beyond the confines of denotational semantics, which all of Jónsson’s eight solution candidates belong to. (shrink)

A property modifier is a function that takes a property to a property. For instance, the modifier short takes the property being a Dutchman to the property being a short Dutchman. Assume that being a round peg is a property obtained by means of modification, round being the modifier and being a peg the input property. Then how are we to infer that a round peg is a peg? By means of a rule of right subsectivity. How are we to (...) infer that a round peg is round? By means of a rule of left subsectivity. This paper puts forward two rules of left subsectivity. The rules fill a gap in the prevalent theory of property modification. The paper also explains why the rules are philosophically relevant. (shrink)

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. (shrink)

This note sketches how a theory of procedural semantics may offer a solution to the problem of the unity of the proposition. The current revival of the notion of structured meaning has made the problem of propositional unity pressing. The problem, stated in its simplest form, is how an individual a and a property F combine into the proposition P that a is an F; i.e. how two different kinds of objects combine into a third kind of object capable of (...) having properties that neither of its constituents could have. Constraints imposed on P include that P must be capable of being true/false, being known/believed to be true/false, and occurring as argument of propositional connectives, such as entailment. (shrink)

In the paper we offer a logical explication of the frequently used, but rather vague, notion of point of view. We show that the concept of point of view prevents certain paradoxes from arising. A point of view is a means of partial characterisation of something. Thus nothing is a P and at the same time a non-P, because it is a P only relative to some point of view and a non-P from another point of view. But there is (...) a major, complicating factor involved in applying a logical method that is supposed to provide a formal and rigorous counterpart of the intuitively understood notion: ‘point of view’ is a homonymous expression, and so there is not just one meaning that would explain points of view. Yet we propose a common scheme of the logical type of the entities denoted by the term ‘point of view’. It is an empirical function: when applied to the viewed object in question, it results in a evaluating proposition about the object. If there is an agent applying the criterion, the result is the agent’s attitude to the respective object. The paper is organised into two parts. In Part I we first adduce and analyse various examples of typical cases of applying a point of view to prevent paradox. These cases are examined according to the type of the viewed object: a) the viewed object is an individual and b) the viewed object is a property or an office. In Part II we then show that the method described in Part I can be applied also to the analyses of agents’ attitudes. We explain how an agent can believe of something that it is a P and at the same time a non-P: the agent applies different viewpoint criteria to the viewed object. The inversion of perspective consisting in the perspective shifting from the believer on to the reporter in the case of attitudes de re, and from the reporter to the believer in the case of attitudes de dicto, is also analyzed. We show that there is no smooth logical traffic back and forth between such attitudes unless some additional assumptions are added, and prove that they are not equivalent. By way of conclusion, we explicate the notion of conceptual point of view and analyze cases of viewpoints given by conceptual distinction. We show, finally, that the proposed scheme of the type of point of view can be preserved, this time, however, in its extensional version. (shrink)

In the paper we offer a logical explication of the frequently used, but rather vague, notion of point of view. We show that the concept of point of view prevents certain paradoxes from arising. A point of view is a means of partial characterisation of something. Thus nothing is a P and at the same time a non-P , because it is a P only relative to some point of view and a non-P from another point of view. But there (...) is a major, complicating factor involved in applying a logical method that is supposed to provide a formal and rigorous counterpart of the intuitively understood notion: ‘point of view’ is a homony-mous expression, and so there is not just one meaning that would explain points of view. Yet we propose a common scheme of the logical type of the entities denoted by the term ‘point of view’. It is an empirical function: when applied to the viewed object in question, it results in a evaluating proposition about the object. If there is an agent applying the criterion, the result is the agent’s attitude to the respective object. The paper is organised into two parts. In Part I we first adduce and analyse various examples of typical cases of applying a point of view to prevent paradox. These cases are examined according to the type of the viewed object: a) the viewed object is an individual and b) the viewed object is a property or an office. In Part II we then show that the method described in Part I can be applied also to the analyses of agents’ attitudes. We thus explain how an agent can believe of something that it is a P and at the same time a non-P: the agent applies different viewpoint criteria to the viewed object. The inversion of perspective consisting in the perspective shifting from the believer on to the reporter in the case of attitudes de re, and from the reporter to the believer in the case of attitudes de dicto, is also analyzed. We show that there is no smooth logical traffic back and forth between such attitudes and prove that they are not equivalent. By way of conclusion, we explicate the notion of conceptual point of view and analyze cases of viewpoints given by conceptual distinction. We show, finally, that the proposed scheme of the type of point of view can be preserved, this time, however, in its extensional version. (shrink)

Nunberg maintains that there are cases like “I am traditionally entitled to a last meal”, as uttered by a condemned prisoner facing the firing squad, which suggest that an indexical like ‘I’ does double duty as a vehicle of singular and general reference. I argue against this claim. My position is that the sentence should be factored out into two: “Traditionally, a condemned prisoner is entitled to a last meal” and “I am a condemned prisoner”. Nunberg’s sentence is generated by (...) means of an illicit substitution of ‘I’ for ‘a condemned prisoner’ inside the scope of ‘traditionally’. The morale is that sloppy or literally nonsensical speech like Nunberg’s sentence is not suitable as data for logical analysis of natural language. What is suitable data is the two-premise argument I put forward. (shrink)

This Festschrift is in honour of Professor Marie Duzí, VSB - Technical University of Ostrava. The 16 contributions, authored by 24 colleagues, run the gamut from foundations in logic and theoretical computer science through philosophical logic, multi-agent systems and theory of communication to personal recollections. Marie Duzí is best known for her profound and extensive work on both the foundations and multiple applications of Transparent Intensional Logic, originally developed by Pavel Tichý in the late 1960s. Her work, whether single-authored or (...) co-authored, has appeared in various high-level journals. In 2008 the Rector of her home university granted Marie the award Outstanding Results in the Development of Science and Research. The 2010 monograph Procedural Semantics for Hyperintensional Logic earned Marie and her coauthors the prestigious Award for Outstanding Results of Major Scientific Importance from the Academy of Sciences of the Czech Republic. The major achievements of Transparent Intensional Logic that Marie has been involved in over the last decade have been compiled into the volume Transparent Intensional Logic: Selected Recent Essays, also published by College Publications. (shrink)