The incommensurability of two theories seems to problematize theory comparisons, which allow for the selection of the better of the two theories. If so, it becomes puzzling how the quality of theories can improve with time, i.e. how science can progress across changes in incommensurable theories. I argue that in papers published in the 1990s, Kuhn provided a novel way to resolve this apparent tension between incommensurability and scientific progress. He put forward an account of their compatibility which worked (...) not by downplaying the negative consequences of incommensurability but instead by allowing them to reach their natural end: a process of specialisation. This development in Kuhn’s thought has yet to be properly recorded but it is also interesting in its own right. It shows how a robust version of incommensurability—one which really does have severe negative consequences for scientists’ capacity to perform comparative evaluations of incommensurable theories—need make no puzzle of the progress of science. (shrink)

Over the last two decades, semantic theory has been marked by a continuing shift from a static view of meaning to a dynamic one. The increasing interest in extending semantic analysis from isolated sentences to larger units of discourse has fostered the intensive study of anaphora and coreference, and this has engendered a shift from viewing meaning as truth conditions to viewing it as the potential to change the "informational context".

I propose a unified solution to two puzzles: Ross's puzzle and free choice permission. I begin with a pair of cases from the decision theory literature illustrating the phenomenon of act dependence, where what an agent ought to do depends on what she does. The notion of permissibility distilled from these cases forms the basis for my analysis of 'may' and 'ought'. This framework is then combined with a generalization of the classical semantics for disjunction — equivalent to (...) Boolean disjunction on the diagonal, but with a different two-dimensional character — that explains the puzzling facts in terms of semantic consequence. (shrink)

This paper investigates the prospects for a semantic theory that treats disjunction as a modal operator. Potential motivation for such a theory comes from the way in which modals embed within disjunctions. After reviewing some of the relevant data, I go on to distinguish a variety of modal theories of disjunction. I analyze these theories by considering pairs of conflicting desiderata, highlighting some of the tradeoffs they must face.

We introduce new algebraic and topological semantics for inquisitive logic. The algebraic semantics is based on special Heyting algebras, which we call inquisitive algebras, with propositional valuations ranging over only the ¬¬-fixpoints of the algebra. We show how inquisitive algebras arise from Boolean algebras: for a given Boolean algebra B, we define its inquisitive extension H(B) and prove that H(B) is the unique inquisitive algebra having B as its algebra of ¬¬-fixpoints. We also show that inquisitive algebras determine Medvedev’s logic (...) of finite problems. In addition to the algebraic characterization of H(B), we give a topological characterization of H(B) in terms of the recently introduced choice-free duality for Boolean algebras using so-called upper Vietoris spaces (UV-spaces). In particular, while a Boolean algebra B is realized as the Boolean algebra of compact regular open elements of a UV-space dual to B, we show that H(B) is realized as the algebra of compact open elements of this space. This connection yields a new topological semantics for inquisitive logic. (shrink)

This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premises. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, and Magidor (1990) and Makinson (1989), (1993). A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred ones. (...) A proposition α is a nonmonotonic consequence of a set of propositions Γ iff α holds in all the most preferred Γ-states. In the literature on revealed preference theory, there are a number of well-known theorems concerning the representability of selection functions, satisfying certain properties, in terms of underlying preference relations. Such theorems are utilized here to give corresponding representation theorems for nonmonotonic inference operations. At the end of the paper, the connection between nonmonotonic inference and belief revision, in the sense of Alchourrón, Gärdenfors, and Makinson, is explored. In this connection, infinitary belief revision operations that allow for the revision of a theory with a possibly infinite set of propositions are introduced and characterized axiomatically. (shrink)

Lewis, D. Semantic analyses for dyadic deontic logic.--Salomaa, A. Some remarks concerning many-valued propositional logics.--Chellas, B. F. Conditional obligation.--Jeffrey, R.C. Remarks on interpersonal utility theory.--Hintikka, J. On the proper treatment of quantifiers in Montague semantics.--Mayoh, B.H. Extracting information from logical proofs.--Åqvist, L. A new approach to the logical theory of actions and causality.--Pörn, I. Some basic concepts of action.--Bouvère, K. de. Some remarks concerning logical and ontological theories.--Hacking, I. Combined evidence.--Äberg, C. Solution to a problem raised by (...) Stig Kanger and a set theoretical statement equivalent to the axiom of choice.--Lindström, P. On characterizing elementary logic.-- Scott, D. Rules and derived rules.--Hansson, B. A program for pragmatics.--Hermerén, G. Models.--Fenstad, J.E. Remarks on logic and probability.--Stenlund, S. Analytic and synthetic arithmetical statements. (shrink)

In his recent paper, “Justice as Fairness: Political not Metaphysical,” John Rawls makes use of a footnote to disown what to many readers must have seemed one of the most striking and original underlying ideas of his theory of justice, that it “is a part, perhaps the most significant part, of the theory of rational choice.” That Rawls should issue this disclaimer indicates, at least in my view, that he has a much clearer understanding of his (...) class='Hi'>theory, and its relationship to rational choice than he did at the time that he wrote A Theory of Justice. As I note in Morals by Agreement, Rawls does not show that principles of justice are principles of rational choice. Hence, in appropriating the idea, I can claim diat I am undertaking a pioneering enterprise. No doubt Thomas Hobbes would have undertaken it had the resources of the theory of rational choice been at his disposal, but I do not intend to pursue counterfactuals in a search for historical antecedents. Moral theory as rational choice theory is, I claim, a new venture. (shrink)

A modified version of Normann's hierarchy of domains with totality [9] is presented and is shown to be suitable for interpretation of Martin-Löf's intuitionistic type theory. This gives an interpretation within classical set theory, which is natural in the sense that $\Sigma$ -types are interpreted as sets of pairs and $\Pi$ -types as sets of choice functions. The hierarchy admits a natural definition of the total objects in the domains, and following an idea of Berger [3] this (...) makes possible an interpretation where a type is defined to be true if its interpretation contains a total object. In particular, the empty type contains no total objects and will therefore be false (in any non-empty context). In addition, there is a natural equivalence relation on the total objects, so we derive a hierarchy of topological spaces (quotient spaces wrt. the Scott topology), and give a second interpretation using this hierarchy. (shrink)

Research using the intermodal preferential looking paradigm (IPLP) has consistently shown that English‐learning children aged 2 can associate transitive argument structure with causal events. However, studies using the same methodology investigating 2‐year‐old children’s knowledge of the conjoined agent intransitive and semantic role assignment have reported inconsistent findings. The aim of the present study was to establish at what age English‐learning children have verb‐general knowledge of both transitive and intransitive argument structure using a new method: the forced‐choice pointing paradigm. (...) The results suggest that young 2‐year‐olds can associate transitive structures with causal (or externally caused) events and can use transitive structure to assign agent and patient roles correctly. However, the children were unable to associate the conjoined agent intransitive with noncausal events until aged 3;4. The results confirm the pattern from previous IPLP studies and indicate that children may develop the ability to comprehend different aspects of argument structure at different ages. The implications for theories of language acquisition and the nature of the language acquisition mechanism are discussed. (shrink)

A disjunctive sentence like Olivia took Logic or Algebra conveys that Olivia didn’t take both classes and that the speaker doesn’t know which of the two classes she took. The corresponding sentence with a possibility modal, Olivia can take Logic or Algebra, conveys instead that she can take Logic and that she can take Algebra. These exclusivity, ignorance and free choice inferences are argued by many to be scalar implicatures. Recent work has looked at cases in which exclusivity and (...) ignorance appear to be computed instead at the presupposition level, independently from the assertion. On the basis of those data, Spector and Sudo :473–517, 2017) have argued for a hybrid account relying on a pragmatic principle for deriving implicatures in the presupposition. In this paper, we observe that a sentence like Noah is unaware that Olivia can take Logic or Algebra has a reading on which free choice appears in the presupposition, but not in the assertion, and we show that deriving this reading is challenging on Spector and Sudo’s hybrid account. Following the dialectic in Fox, we argue against a pragmatic approach to presupposition-based implicatures on the ground that it is not able to account for presupposed free choice. In addition, we raise a novel challenge for Spector and Sudo’s account coming from the conflicting presupposed ignorance triggered by sentences like #Noah is unaware that I have a son or a daughter, which is infelicitous even if it’s not common knowledge whether the speaker has a son or a daughter. More generally, our data reveals a systematic parallelism between the assertion and presupposition levels in terms of exclusivity, ignorance, and free choice. We argue that such parallels call for a unified analysis and we sketch how a grammatical theory of implicatures where meaning strengthening operates in a similar way at both levels :31–57, 2012; Magri in A theory of individual-level predicates based on blind mandatory scalar implicatures, MIT dissertation, 2009; Marty in Implicatures in the DP domain, MIT dissertation, 2017) can account for such parallels. (shrink)

This paper develops a semantic solution to the puzzle of Free Choice permission. The paper begins with a battery of impossibility results showing that Free Choice is in tension with a variety of classical principles, including Disjunction Introduction and the Law of Excluded Middle. Most interestingly, Free Choice appears incompatible with a principle concerning the behavior of Free Choice under negation, Double Prohibition, which says that Mary can’t have soup or salad implies Mary can’t have (...) soup and Mary can’t have salad. Alonso-Ovalle 2006 and others have appealed to Double Prohibition to motivate pragmatic accounts of Free Choice. Aher 2012, Aloni 2018, and others have developed semantic accounts of Free Choice that also explain Double Prohibition. -/- This paper offers a new semantic analysis of Free Choice designed to handle the full range of impossibility results involved in Free Choice. The paper develops the hypothesis that Free Choice is a homogeneity effect. The claim possibly A or B is defined only when A and B are homogenous with respect to their modal status, either both possible or both impossible. Paired with a notion of entailment that is sensitive to definedness conditions, this theory validates Free Choice while retaining a wide variety of classical principles except for the transitivity of entailment. The homogeneity hypothesis is implemented in two different ways, homogeneous alternative semantics and homogeneous dynamic semantics, with interestingly different consequences. (shrink)

Free Choice is the principle that possibly p or q implies and is implied by possibly p and possibly q. A variety of recent attempts to validate Free Choice rely on a nonclassical semantics for disjunction, where the meaning of p or q is not a set of possible worlds. This paper begins with a battery of impossibility results, showing that some kind of nonclassical semantics for disjunction is required in order to validate Free Choice. The paper (...) then provides a positive account of Free Choice, by identifying a family of dynamic semantics for disjunction that can validate the inference. On all such theories, the meaning of p or q has two parts. First, p or q requires that our information is consistent with each of p and q. Second, p or q narrows down our information by eliminating some worlds. It turns out that this second component of or is well behaved: there is a strongest such meaning that p or q can express, consistent with validating Free Choice. The strongest such meaning is the classical one, on which p or q eliminates any world where both p and q are false. In this way, the classical meaning of disjunction turns out to be intimately related to the validity of Free Choice. (shrink)

In his late philosophy, Quine generalized the structuralist view in the philosophy of mathematics that mathematical theories are indifferent to the ontology we choose for them. According to his ‘global structuralism’, the choice of objects does not matter to any scientific theory. In the literature, this doctrine is mainly understood as an epistemological thesis claiming that the empirical evidence for a theory does not depend on the choice of its objects. The present paper proposes a new (...) interpretation suggested by Quine’s recently published Kant Lectures from 1980 according to which his global structuralism is a semantic thesis that belongs to his theory of ontological reduction. It claims that a theory can always be reformulated in such a way that its truth does not presuppose the existence of the original objects, but only of some objects that can be considered as their proxies. Quine derives this claim from the principle of the semantic primacy of sentences, which is supposed to license the ontological reductions he uses to establish his global structuralism. It is argued that these reductions do not actually work because they do not account for some hidden ontological commitments that are not detected by his criterion of ontological commitment. (shrink)

Among the most important of Sten Lindström’s achievements in philosophy and logic is that he was the first researcher to realise that the theory of rational choice can be brought to bear in the domain of logic and reasoning. The new conception was that a sentence α is a consequence of a set of sentences Γ just in case α is true in all selected ("best", "most plausible") possible worlds in which all sentences in Γ are true (rather (...) than in all possible worlds in which all sentences in Γ are true). And the selection of possible worlds should conform to the constraints on rational choices. Sten worked out this idea in stunning depth, detail and precision in his seminal paper "A semantic approach to nonmonotonic reasoning: Inference operations and choice." The paper was ready in draft form in April 1991 and presented in two talks later that year. It was included, in almost the same form, in the report series Uppsala Prints and Preprints in Philosophy in 1994, but it was never regularly published. The 2022 publication in Theoria seeks to compensate for this omission. (shrink)

Recent work on mood choice considers fine-grained semantic differences among desire predicates (notably, ‘want’ and ‘hope’) and their consequences for the distribution of indicative and subjunctive complement clauses. In that vein, this paper takes a close look at ‘intend’. I show that cross-linguistically, ‘intend’ accepts nonfinite and subjunctive complements and rejects indicative complements. This fact poses difficulties for recent approaches to mood choice. Toward a solution, a broad aim of this paper is to argue that—while ‘intend’ is (...) loosely in the family of desire predicates—it differs from ‘want’ and ‘hope’ in that it has a causative component, and this is relevant to its mood choice behavior, given that causative predicates also systematically reject indicative complements. More concretely, my analysis has three ingredients: (i) following related proposals in philosophy, intention reports have causally self-referential content; (ii) encoding causal self-reference requires abstraction over the complement clause’s eventuality argument; and (iii) nonfinite and subjunctive clauses enable such abstraction but indicative clauses do not. Aside from causative predicates, independent support for the proposal comes from the syntax of belief-/intention-hybrid attitude predicates like ‘decide’ and ‘convince’, anankastic conditional antecedents, aspectual predicates, and memory and perception reports. Synthesizing this result with that of previous literature, the emergent generalization is that subjunctive mood occurs in attitude reports that involve either comparison or eventuality abstraction. Toward a unified theory of mood choice, I suggest that both comparison and eventuality abstraction represent departures from the clausal semantics of unembedded assertions and consequently that subjunctive mood signals such a departure. (shrink)

This book, first published in 1987, investigates what distinguishes the part of human behaviour that is action from the part that is not. The distinction was clearly drawn by Socrates, and developed by Aristotle and the medievals, but key elements of their work became obscured in modern philosophy, and were not fully recovered when, under Wittgenstein’s influence, the theory of action was revived in analytical philosophy. This study aims to recover those elements, and to analyse them in terms of (...) a defensible semantics on Fregean lines. Among its conclusions: that actions are bodily or mental events that are causally explained by their doers’ propositional attitudes, especially by their choices or fully specific intentions; that choice cannot be reduced to desire and belief, and hence that the traditional concept of will as intellectual appetite must be revived. (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and (...) in theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (2nd Edition), Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects, J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. (shrink)

Standard semantics of proper names assigns them the function of reference to individual things. This presupposes that to understand the meaning of a proper name is to understand what it denotes in the context of its referential use. But unambiguous identification of the referent of a proper name in its normal (referential) use looks like an unsolvable problem. Senses associated with referential uses of such names don't allow ascribing them singular referents in their contexts; and what concerns contexts themselves, they (...) either don't contain proper referents at all or contain more than one, thus being referentially ambiguous. Some philosophers of language believe that the main problem for the standard semantics of proper names is that they assign them referents of wrong kind: that these, for instance, should be rather abstract entities, i.e. sets, than individual things. In this paper I try to argue that the choice of an alternative semantics for proper names does not solve the main problem with their meanings, i.e. that of their referential ambiguity. On the one hand even in the most transparent contexts there is always available an alternative referent to be assigned to the proper name's use along with some standard or default one; the fact that we prefer some standard interpretation (when we actually do) over alternative ones reflects at best that certain semantic theories contribute more substantially to ordinary communication in comparison with others. This does not yet imply that they better explain meanings of proper names. On the other hand there is also no good explanation of a phenomenon of reference to a particular thing as such: we still don't understand how a name may become referring to one and the same particular thing in many different situations for many different agents of its use etc., and how the thing may literally become a bearer of a name. (shrink)

In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a set can be viewed as a "possible world," with the key property of a world being primeness—a world makes a disjunction true only if it makes one of the disjuncts true—which classically implies totality—for each proposition, a world either (...) makes the proposition true or makes its negation true. This chapter surveys a more general approach to logical semantics, known as possibility semantics, which replaces possible worlds with possibly partial "possibilities." In classical possibility semantics, propositions are interpreted as regular open sets of a poset, as in set-theoretic forcing, or as compact regular open sets of an upper Vietoris space, as in the recent theory of "choice-free Stone duality." The elements of these sets, viewed as possibilities, may be partial in the sense of making a disjunction true without settling which disjunct is true. We explain how possibilities may be used in semantics for classical logic and modal logics and generalized to semantics for intuitionistic logics. The goals are to overcome or deepen incompleteness results for traditional semantics, to avoid the nonconstructivity of traditional semantics, and to provide richer structures for the interpretation of new languages. (shrink)

This paper deals with structures ${\langle{\bf T}, I\rangle}$ in which T is a tree and I is a function assigning each moment a partition of the set of histories passing through it. The function I is called indistinguishability and generalizes the notion of undividedness. Belnap’s choices are particular indistinguishability functions. Structures ${\langle{\bf T}, I\rangle}$ provide a semantics for a language ${\mathcal{L}}$ with tense and modal operators. The first part of the paper investigates the set-theoretical properties of the set of indistinguishability (...) classes, which has a tree structure. The significant relations between this tree and T are established within a general theory of trees. The aim of second part is testing the expressive power of the language ${\mathcal{L}}$ . The natural environment for this kind of investigations is Belnap’s seeing to it that (stit). It will be proved that the hybrid extension of ${\mathcal{L}}$ (with a simultaneity operator) is suitable for expressing stit concepts in a purely temporal language. (shrink)

A once commonplace view is that only a semantic theory that interprets sentences of a language according to what their utterances intuitively say can be correct. The rationale is that only by requiring a tight connection between what a sentence means and what its users intuitively say can we explain why, normally, those linguistically competent with a language upon hearing its sentences uttered can discern what they say. More precisely, this approach ties the semantic content of a (...) sentence to intuitions about “says that” reports. Cappelen and Lepore forcefully argued against this approach. But given their criticism, what constraints are there on a correct assignment of semantic conent to sentences of a language? Two choices are available regard: either give up the strategy of identifying semantic content by looking at indirect speech reports, or, conclude that the intuition about the connection between meaning and intuitions about indirect reports is basically on the right track, but needs to be further constrained. We will explore both strategies and argue that ultimately we should reject the intuitions about indirect reports as tests on semantic theory, and propose a more direct strategy for identifying semantic content. (shrink)

Montague (1970) interprets a small fragment of English through the use of two basic types of objects: individuals and propositions. My dissertation develops an alternative semantics that only uses one basic type (hence, *single-type semantics*). Such a semantics has been conjectured by Partee (2006) as a ‘minimality test’ for the Montagovian type system, which captures the lowest ontological requirements on any successful semantics for Montague’s fragment. The development of this semantics answers a number of important open questions about the salience (...) of the Montagovian type system, the robustness of semantic theories w.r.t. their basic-type choice, and the classification of these theories according to their objects’ informational strength. (shrink)

The purpose of this paper is to present some results instit theory, a theory of agency proposed by N. Belnap and M. Perloff. We will establish a correspondence between the numbers ofstit modalities and the complexity degrees ofbusy choice sequences in semantic structures, and consequently, a correspondence between the number of modes of actions/inactions instit theory and the complexity degrees ofbusy choice sequences in semantic structures.

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and (...) in theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism, Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects, J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. (shrink)

Sentences such as Olivia can take Logic or Algebra (‘♢∨-sentences’) are typically interpreted as entailing that Olivia can take Logic and can take Algebra. Given a standard semantics for modals and disjunction, those ‘Free choice’ (FC) readings are not predicted from the surface form of ♢∨-sentences. Yet the standard semantics is appropriate for the ‘double prohibition’ reading typically assigned to ¬♢∨-sentences like Olivia can’t take Logic or Algebra. Several extant approaches to FC can account for those two cases, but (...) face challenges when ♢∨, ¬♢∨ and related sentences appear embedded in certain environments. In this paper, we present a novel account of FC that builds on a ‘grammatical’ theory of scalar implicatures — proposed by Bassi et al. (2021) and Del Pinal (2021) — according to which covert exhaustification is a presupposition trigger such that the prejacent forms the assertive content while any excludable or includable alternatives are incorporated at the non-at issue, presuppositional level. Applied to ♢∨, ¬♢∨, and similar sentences, ‘presuppositional exhaustification’ predicts that their default interpretations have an assertive component (roughly, the classical interpretation of the prejacent) and a homogeneity presupposition which projects in standard ways. Those predictions, we then show, support a uniform account of the puzzling behavior of ♢∨, ¬♢∨, and related sentences when embedded under (negative) factives (Marty & Romoli 2020), disjunctions (Romoli & Santorio 2019), and in the scope of universal, existential (Bar-Lev & Fox 2020) and non-monotonic quantifiers (Gotzner et al. 2020). (shrink)

It is well known that the validity of Choice Principles is problematic in non-standard Set Theories which do not abide by the Limitation of Size Principle. In this paper we discuss the consistency of various Choice Principles with respect to the Generalized Positive Comprehension Principle . The Principle GPC allows to take as sets those classes which can be specified by Generalized Positive Formulae, e.g. the universe. In particular we give a complete characterization of which choice principles (...) hold in Hyperuniverses. Hyperuniverses are structures which arose independently in Non-well-founded Set Theory and in Mathematical Semantics of Concurrent Programming Languages and are hitherto the only existing models of GPC. Hyperuniverses are naturally endowed with a κ-compact uniform κ-topology and are uniformly isomorphic to their exponential space, i.e. the space of their closed subsets endowed with the Exponential Uniformity. (shrink)

Disjunctions in the scope of possibility modals give rise to a conjunctive inference, generally referred to as ‘free choice.’ For example, Emma can take Spanish or Calculus suggests that Emma can take Spanish and can take Calculus. This inference is not valid on standard semantics for modals in combination with a Boolean semantics for disjunction. Hence free choice has sparked a whole industry of theories in philosophy of language and semantics. This paper investigates free choice in sentences (...) involving a non-monotonic modified numeral, under which we embed a possibility modal scoping over disjunction. One example is Exactly one student can take Spanish or Calculus. As we point out, the presence of certain readings of these sentences is a key test for a prominent approach, which analyzes free choice as a kind of scalar implicature. We report on two experiments investigating the readings of such sentences, using an inferential task. Our results are challenging for the implicature approach. We sketch two possible solutions within this approach, either adopting a different recent implicature algorithm, or exploring a different meaning for modified numerals with exactly. Both of them suffer from a variety of problems. We then discuss a third solution, which exploits a recent account of free choice based on homogeneity. This approach can account for our results, in combination with plausible assumptions about homogeneity projection, though it too has open issues with related cases. Regardless of which solution is chosen, non-monotonic contexts turn out to be an important test case for theories of free choice, implicature, and modified numerals. (shrink)

A number of important legal theorists have recently argued for metaphysically realist approaches to legal determinacy grounded in particular semantic theories or theories of reference, in particular, views of meaning and reference based on the works of Putnam and Kripke. The basic position of these theorists is that questions of legal interpretation and legal determinacy should be approached through semantic meaning. However, the role of authority (in the form of lawmaker choice) in law in general, and democratic (...) systems in particular, require that these realist solutions to the problem of legal determinacy be rejected, or at least significantly revised. (shrink)

Among the possible solutions to the paradoxes of collective preferences, single-peakedness is significant because it has been associated to a suggestive conceptual interpretation: a single-peaked preference profile entails that, although individuals may disagree on which option is the best, they conceptualize the choice along a shared unique dimension, i.e. they agree on the rationale of the collective decision. In this article, we discuss the relationship between the structural property of singlepeakedness and its suggested interpretation as uni-dimensionality of a social (...) choice. In particular, we offer a formalization of the relationship between single-peakedness and its conceptual counterpart, we discuss their logical relations, and we question whether single-peakedness provides a rationale for collective choices. (shrink)

Richard Thaler and Cass Sunstein’s Nudge advances a theory of how designers can improve decision-making in various situations where people have to make choices. We claim that the moral acceptability of nudges hinges in part on whether they can provide an account of the competence required to offer nudges, an account that would serve to warrant our general trust in choice architects. What needs to be considered, on a methodological level, is whether they have clarified the competence required (...) for choice architects to prompt subtly our behaviour toward making choices that are in our best interest from our own perspectives. We argue that, among other features, an account of the competence required to offer nudges would have to clarify why it is reasonable to expect that choice architects can understand the constraints imposed by semantic variance. Semantic variance refers to the diverse perceptions of meaning, tied to differences in identity and context, that influence how users interpret nudges. We conclude by suggesting that choice architects can grasp semantic variance if Thaler and Sunstein’s approach to design is compatible with insights about meaning expressed in science and technology studies and the philosophy of technology. (shrink)

It is widely believed that the semantic contents of some linguistic and mental representations are determined by factors independent of a person’s bodily makeup. Arguments derived from Hilary Putnam’s seminal Twin Earth thought experiment have been especially influential in establishing that belief. I claim that there is a neglected version of the mind-body relation which undermines those arguments and also excludes the possibility of zombies. It has been neglected because it is counterintuitive but I show that it can nonetheless (...) be intelligibly worked out in detail and all obvious objections met. This suggests that we may be faced with a choice between embracing a counterintuitive interpretation of the mind-body relation or accepting that a currently very promising theory in cognitive science, Prediction Error Minimization, faces a fundamental problem. Furthermore, blocking that threat entails that any physicalist/materialst theory of mind is freed from the spectre of zombie worlds. The proposal also makes the ideas of personal teleportation of mind uploading more plausible. (shrink)

The paper explores the relativistic implications of the thesis of incommensurability. A semantic form of incommensurability due to semantic variation between theories is distinguished from a methodological form due to variation in methodological standards between theories. Two responses to the thesis of semantic incommensurability are dealt with: the first challenges the idea of untranslatability to which semantic incommensurability gives rise; the second holds that relations of referential continuity eliminate semantic incommensurability. It is then argued that (...) methodological incommensurability poses little risk to the rationality or objectivity of science. For rational theory choice need neither be dictated by an algorithm nor governed by a binding set of rules. The upshot of the discussion is deflationary. There is little prospect for a relativistic conception of science based on inflated claims about the incommensurability of scientific theories. (shrink)

A certain skeptical strategy involves a skeptical hypothesis that closely mirrors the structure of our standard theory of the world; this strategy insulates the skeptical argument from attacks based on standard criteria of theory choice. A standard reply to this strategy is to claim that proffered alternative is just the standard theory expressed in a different notation. But this reply does not succeed, given plausible assumptions about semantics. However, there is an alternative strategy--also semantical--which can deal (...) with the problem, at least in those cases where, intuitively, the skeptic's challenge should fail. (shrink)

Consistency of choice is a fundamental and recurring theme in decision theory, social choice theory, behavioral economics, and psychological sciences. The purpose of this paper is to study the consistency of choice independent of the particular decision model at hand. Consistency is viewed as an inherently logical concept that is fundamentally void of connotation and is thus disentangled from traditional rationality or consistency conditions imposed on decision models. The proposed formalization of consistency takes two forms: (...) internal consistency, which refers to the property that a choice model does not generate contradictory statements; and semantic consistency, which refers to the idea that a theory’s predictions are valid with respect to some observed data. In addressing semantic consistency, the relationship between theory and data is analyzed in terms of so-called duality mappings, which allow a passage between the two universes in a way that consistency is preserved. The formalization of consistency concepts relies on adapting the revealed preference theory to the context-dependent setting. The paper concludes by discussing the implications of the proposed framework and how it relates to classical revealed preference theory and other formalizations of the relationship between the theory and reality of choice. (shrink)

The concept of a linguistic framework and the distinction between internal and external questions are the central ideas of Rudolf Carnap's "Empiricism, Semantics, and Ontology." It is not uncommon to encounter the suggestion that reflection on the theoretical and experimental investigations which led to the acceptance of the atomic hypothesis undermines Carnap's distinction between these two types of question and the utility of his notion of a linguistic framework. I believe this is a mistake. There is a natural development of (...) the distinction and the notion of framework choice with which it is paired that is perfectly capable of accommodating this case. I show this by bringing out a subtlety that arises in the extension of the con ceptual apparatus of ESO to the realism/instrumentalism controversy. When this subtlety is taken into account, the question contested by the nineteenth- and early twentieth-century opponents and proponents of the atomic hypothesis, and successfully addressed by Einstein and Perrin, is readily seen to be internal. Moreover, this formulation of the distinction and the controversy are both independent of Carnap's views on cognitive significance and factual content. I conclude with a presentation and discussion of two formulations of the realism/instrumentalism controversy that are based on Carnap's explication of the factual content of a theory in terms of the notion of its Ramsey sentence. (shrink)

Richard Thaler and Cass Sunstein’s Nudge advances a theory of how designers can improve decision-making in various situations where people have to make choices. We claim that the moral acceptability of nudges hinges in part on whether they can provide an account of the competence required to offer nudges, an account that would serve to warrant our general trust in choice architects. What needs to be considered, on a methodological level, is whether they have clarified the competence required (...) for choice architects to prompt subtly our behaviour toward making choices that are in our best interest from our own perspectives. We argue that, among other features, an account of the competence required to offer nudges would have to clarify why it is reasonable to expect that choice architects can understand the constraints imposed by semantic variance. Semantic variance refers to the diverse perceptions of meaning, tied to differences in identity and context, that influence how users interpret nudges. We conclude by suggesting that choice architects can grasp semantic variance if Thaler and Sunstein’s approach to design is compatible with insights about meaning expressed in science and technology studies and the philosophy of technology. (shrink)

We started from the fact that type theory, in the way it was implemented in IL, makes it costly to deal with nominalization processes. We have also argued that the type hierarchy as such doesn't play any real role in a grammar; the classification it provides for different semantic objects is already contained, in some sense, in the categorial structure of the grammar itself. So, on the basis of a theory of properties (Cocchiarella's HST*) we have tried (...) to build a language (IL*) whose syntax does not contain any explicit typing of expressions. Some of the consequences that this move brings about in the overall organization of the grammar can be summarized as follows:it allows for a simple treatment of infinitives, gerunds, factives and, in general, all those phenomena which might be analyzed as cases of nominalization;it provides a simpler and more constrained semantics than IL, since IL* doesn't go beyond second order, and its non-modal basis is axiomatizable;it suggests that the role of logical form in a theory of grammar could be that of a family of theories of semantic objects;it eliminates the extrinsic limitations of a type hierarchy on the choice of the system of syntactic categories.I think that it is interesting to notice how having an explicit semantic framework helps to provide a sense in which it is legitimate to regard the syntax of a language as ‘autonomous’. (shrink)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection (...) of sentences, above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

The idea to use choice functions in the semantic analysis of indefinites has recently gained increasing attention among linguists and logicians. A central linguistic motivation for the revived interest in this logical perspective, which can be traced back to the epsilon calculus of Hilbert and Bernays (1939), is the observation by Reinhart (1992,1997) that choice functions can account for the problematic scopal behaviour of indefinites and interrogatives. On-going research continues to explore this general thesis, which I henceforth (...) adopt. In this paper I would like to address the matter from two angles. First, given that the semantics of indefinites involves functions, it still does not follow that these have to be choice functions. The common practise is to stipulate this restriction in order to get existential semantics right. However, a so-far open question is whether there is any way to derive choice function interpretation from more general principles of natural language semantics. Another question that has not been formally accounted for yet concerns the relationships between choice functions and the ``specificity'' ``referentiality'' intuition of Fodor and Sag (1981) about indefinites. Is there a sense in which choice functions capture this popular pre-theoretical notion? In order to answer these questions, this paper proposes a revision in the treatment of choice functions in Winter (1997), leaving its linguistic predictions unaffected but changing slightly the compositional mechanism. This modification opens the way for proving the following theorem: function variables in the analysis of the noun phrase must denote only choice functions and can derive only the standard existential analysis by virtue of the conservativity, logicality and non-triviality universals of Generalized Quantifier Theory as proposed in Barwise and Cooper (1981), Van Benthem (1984), Thijsse (1983) and others. The same implementation also captures the ``specificity'' notion: indefinites with a non-empty restriction set denote principal ultrafilters in the revised formalization. These are the quantificational correlates to ``referential'' individuals.. (shrink)

In the present paper we confront Martin- Löf’s analysis of the axiom of choice with J. Hintikka’s standing on this axiom. Hintikka claims that his game theoretical semantics for Independence Friendly Logic justifies Zermelo’s axiom of choice in a first-order way perfectly acceptable for the constructivists. In fact, Martin- Löf’s results lead to the following considerations:Hintikka preferred version of the axiom of choice is indeed acceptable for the constructivists and its meaning does not involve higher order logic.However, (...) the version acceptable for constructivists is based on an intensional take on functions. Extensionality is the heart of the classical understanding of Zermelo’s axiom and this is the real reason behind the constructivist rejection of it.More generally, dependence and independence features that motivate IF-Logic, can be formulated within the frame of constructive type theory without paying the price of a system that is neither axiomatizable nor has an underlying theory of inference – logic is about inference after all.We conclude pointing out that recent developments in dialogical logic show that the CTT approach to meaning in general and to the axiom of choice in particular is very natural to game theoretical approaches where metalogical features are explicitly displayed at the object language-level. Thus, in some way, this vindicates, albeit in quite of a different manner, Hintikka’s plea for the fruitfulness of game-theoretical semantics in the context of the foundations of mathematics. (shrink)

Proof-theoretic semantics is an inferentialist theory of meaning, usually developed in a multiple-assumption and single-conclusion framework. In that framework, this theory seems unable to justify classical logic, so some authors have proposed a multiple-conclusion reformulation to accomplish this goal. In the first part of this paper, the debate originated by this proposal is briefly exposed and used to defend the diverging opinion that proof-theoretic semantics should always endorse a single-assumption and single-conclusion framework. In order to adopt this approach (...) some of its _criteria_ of validity, especially separability, need to be weakened. This choice is evaluated and defended. The main argument in this direction is based on the circular dependences of meaning between multiple assumptions and conjunctions, and between multiple conclusions and disjunctions. In the second part of this paper, some systems that suit the new requirements are proposed for both intuitionistic and classical logic. A proof that they are valid, according to the weakened _criteria_, is sketched. (shrink)

The relevance of the research is defined by the need to create a set of linguistic means, which would contribute to effective communication with the general public, and the need to study different functional-semantic categories, including appeals, for the competent formation of public opinion in the political context. The research aims to comprehend the functioning of linguistic means used as appeals in the example of political propaganda texts in the English media field. The methodology is based on the theoretical (...) study of the works of modern linguists, linguistic, structural, and communicative analysis of appeal linguistic units and contexts. The research considered the linguistic means that form the functional-semantic category of the appeal, examples of political contexts from the British and American media were presented, the functions of appeal were presented using specific examples, an idea of the communicative side of political propaganda texts and audience participation in this process was formed, emphasis was placed on different types of propaganda (white, black, gray), the following groups of appeals were characterized: imperatives (volitional and involuntary). The materials presented in this research can be used to form an idea of the functional-semantic category of appeal, the choice of linguistic means for the purpose of information promotion in the media or social networks, the study of communicative strategies in linguistics and their successful implementation, consideration of political propaganda texts, increasing efficiency when influencing the audience, further implementation of means of appeal in machine learning. (shrink)

This paper describes semantic communication as an arbitrary loss function. I reject the logical approach to semantic information theory described by Carnap, Bar-Hillel and Floridi, which assumes that semantic information is a logical function of Shannon information mixed with categorical objects. Instead, I follow Hirotugu Akaike’s maximum entropy approach to model semantic communication as a choice of loss. The semantic relationship between a thing and a message about the thing is modelled as the (...) loss of information that results in the impression contained in the message, so that the semantic meaning of a bear’s footprint is the difference between the actual bear and its footprint. Experience has a critical function in semantic meaning because a bear footprint can only be meaningful if we have some experience with an actual bear. The more direct our experience, the more vivid the footprint will appear. In this model, what is important is not the logic of the categories represented by the information but the loss of information that reduces our experiences of reality to functional communication. The hard problem of semantic communication arises because real objects and events do not come with categorical labels attached, so the choice of loss is necessarily imperfect and illogical. (shrink)

Modal logic has been used to analyze potential infinity and potentialism more generally. However, the standard analysis breaks down in cases of divergent possibilities, where there are two or more possibilities that can be individually realized but which are jointly incompatible. This paper has three aims. First, using the intuitionistic theory of choice sequences, we motivate the need for a modal analysis of divergent potentialism and explain the challenges this involves. Then, using Beth–Kripke semantics for intuitionistic logic, we (...) overcome those challenges. Finally, we apply our modal analysis of divergent potentialism to make choice sequences comprehensible in classical terms. (shrink)

The aim of this paper is to compare two approaches to semantics, namely the standard Tarskian theory and Wittgenstein’s picture theory of meaning. I will compare them with respect to an unusual subject matter, namely to geometrical pictures. The choice of geometry rather than arithmetic or set theory as the basis, on which this comparison will be made has two reasons. One reason is related to Wittgenstein’s picture theory of meaning. This theory was developed (...) more or less as a metaphor, comparing the language to a picture. Nevertheless, if we take pictures themselves in the role of the language to which we apply Wittgenstein’s picture theory of meaning, this theory stops being a metaphor and starts to work in a technical way. I believe that in this way we can create a new approach to semantics in geometry. The other reason for taking geometry as the basis for our investigation is that the Tarskian approach to semantics does not work in geometry as we would wish. (shrink)