This book pursues the question of how and whether natural language allows for reference to abstract objects in a fully systematic way. By making full use of contemporary linguistic semantics, it presents a much greater range of linguistic generalizations than has previously been taken into consideration in philosophical discussions, and it argues for an ontological picture is very different from that generally taken for granted by philosophers and semanticists alike. Reference to abstract objects such as properties, numbers, (...) propositions, and degrees is considerably more marginal than generally held. (shrink)

Wójcicki has provided a characterization of selfextensional logics as those that can be endowed with a complete local referential semantics. His result was extended by Jansana and Palmigiano, who developed a duality between the category of reduced congruential atlases and that of reduced referential algebras over a fixed similarity type. This duality restricts to one between reduced atlas models and reduced referential algebra models of selfextensional logics. In this paper referential algebraic systems and congruential atlas systems are introduced, which (...) abstract referential algebras and congruential atlases, respectively. This enables the formulation of an analog of Wójcicki’s Theorem for logics formalized as π-institutions. Moreover, the results of Jansana and Palmigiano are generalized to obtain a duality between congruential atlas systems and referential algebraic systems over a fixed categorical algebraic signature. In future work, the duality obtained in this paper will be used to obtain one between atlas system models and referential algebraic system models of an arbitrary selfextensional π-institution. Using this latter duality, the characterization of fully selfextensional deductive systems among the selfextensional ones, that was obtained by Jansana and Palmigiano, can be extended to a similar characterization of fully selfextensional π-institutions among appropriately chosen classes of selfextensional ones. (shrink)

Here, we defend the thesis whereby the event plays a main role of sense in the meaning of certain sentences. This thesis is based on the one hand on recent work in the metaphysics of so-called “happening” entities, which has led to a distinction between concrete physical processes and abstract events, the latter being conceived as psychological constructs accounting for stabilities or changes in the world. Furthermore, we look back at the work on intentionality carried out in the Brentanian (...) school at the turn of the 20th century and we relate abstract events to the mental states of affairs studied by Twardowski but which were then neglected by contemporary philosophers of language. Abstract events, thus characterized, have the contingent property of occurring, when facts obtain and realize them. We suggest that the facts in question correspond to Wittgensteinian states of affairs. (shrink)

Affective information can be retrieved simply by measuring words co‐occurrences in linguistic contexts. Lenci and colleagues demonstrate that the affective measures retrieved from linguistic occurrences predict words’ concreteness: abstract words are more heavily loaded with affective information than concrete ones. These results challenge the Affective grounding hypothesis, suggesting that abstract concepts may be ungrounded and coded only linguistically, and that their affective load may be a linguistic factor.

Alonzo Church has repeatedly argued that the semantic analysis of certain contexts requires reference to abstract entities of various kinds. The problem, arising from this argument for nominalists, will be examined first. Then we shall attempt to meet Church’s challenge by constructing and informally describing a semantics which was inspired by Nelson Goodman’s distinction between primary and secondary extensions. According to that semantics, no expression of the object language will make reference to any abstract or non-actual (...) entity while the system is strong enough to lend itself to semantic analysis in Church’s sense. (shrink)

This book presents a study of meaning relations, linking the philosophical tradition of conceptual analysis with recent theories and methodologies in cognitive semantics. Its main concern is the extent to which analyzing meaning relations between cognate words reveal the infrastructure of the actual and mental lexicon, assuming that language mirrors thought. Sovran aims to elucidate their infrastructure and the metaphorical and perceptual models that constitute abstract concepts, dealing finally with the role of abstraction in poetic metaphors. Overall, this (...) volume addresses major contemporary issues in the philosophy of language and theoretical semantics. (shrink)

We define and study abstract valuation semantics for logics, an algebraically well-behaved version of valuation semantics. Then, in the context of the behavioral approach to the algebraization of logics, we show, by means of meaningful bridge theorems and application examples, that abstract valuations are suited to play a role similar to the one played by logical matrices in the traditional approach to algebraization.

This work adapts techniques and results first developed by Malinowski and by Marek in the context of referential semantics of sentential logics to the context of logics formalized as π-institutions. More precisely, the notion of a pseudoreferential matrix system is introduced and it is shown how this construct generalizes that of a referential matrix system. It is then shown that every π–institution has a pseudo-referential matrix system semantics. This contrasts with referential matrix system semantics which is only (...) available for self-extensional π-institutions by a previous result of the author obtained as an extension of a classical result of Wójcicki. Finally, it is shown that it is possible to replace an arbitrary pseudoreferential matrix system semantics by a discrete pseudo-referential matrix system semantics. (shrink)

Abstract: According to certain dispositional accounts of meaning, an agent's meaning is determined by the dispositions that an idealized version of this agent has in optimal conditions. We argue that such attempts cannot properly fix meaning. For even if there is a way to determine which features of an agent should be idealized without appealing to what the agent means, there is no non-circular way to determine how those features should be idealized. We sketch an alternative dispositional account that (...) avoids this problem, according to which an agent's meaning is determined by the dispositions that an abstract version of this agent has in optimal conditions. (shrink)

Since their introduction by Partee and Rooth (1983) into linguistic theory, type shifting principles have been extensively employed in various linguistic domains, including nominal predicates (Partee 1987), kind denoting NPs (Chierchia 1998), interrogatives (Groenendijk and Stokhof 1989), scrambled definites (De Hoop and Van der Does 1998) and plurals (Winter 2001,2002). Most of the accounts that use type shifting principles employ them as ``last resort'' mechanisms, which apply only when other compositional mechanisms fail. This failure is often sloppily referred to as (...) type mismatch . The motivation for introducing type mismatch into the compositional mechanism is twofold: on the one hand it allows lexical items to be assigned the minimal types that are needed for describing their denotation; on the other hand, it has been argued that the ``last resort'' strategy of type shifting prevents derivation of undesired meanings. The first goal of this paper is to define a simple notion of type mismatch, which will rather closely follow Partee and Rooth's original proposal but will be expressed within more familiar terms of categorial semantics. After introducing this implementation of traditional type mismatch, it will be argued that in fact, it covers only one possible kind of trigger for type shifting principles. Partee and Rooth's notion of mismatch is ``external'' in that the type of an expression is changed only when it combines with another type to which it cannot compose using the ``normal'' compositional mechanism. It will be argued that, within an appropriate type system, another notion of mismatch is also useful. This is the kind of mismatch in which the semantic type of an expression does not match its syntactic category. Two such cases will be explored: mismatch between morpho-syntactic number (singular or plural) and semantic number (a denotation ranging over atoms or sets), and mismatch between syntactic category (noun, DP, adjective etc.) and semantic role (predicate, quantifier, predicate modifier etc.).. (shrink)

According to the neo-Fregean abstractionism, numerical expressions of the form ‘the number of Fs’, introduced by Hume’s Principle, should be read as purportedly referential singular terms. I will explore the prospects of a version of abstractionism in which such expressions have presuppositional content, as in Strawson’s account. I will argue that the thesis that ‘the number of Fs’ semantically presupposes the existence of a number is inconsistent with the required ‘modest’ stipulative character of the truth of Hume’s Principle: since Hume’s (...) Principle is true and provably presupposes that numbers exist, what it presupposes is also true; and so numbers exist. This, however, means that numbers are conjured into existence by a direct stipulation. (shrink)

According to certain kinds of semantic dispositionalism, what an agent means by her words is grounded by her dispositions to complete simple tasks. This sort of position is often thought to avoid the finitude problem raised by Kripke against simpler forms of dispositionalism. The traditional objection is that, since words possess indefinite (or infinite) extensions, and our dispositions to use words are only finite, those dispositions prove inadequate to serve as ground for what we mean by our words. I argue (...) that, even if such positions (emphasizing simple tasks) avoid the traditional form of Kripke's charge, they still succumb to special cases of the finitude problem. Furthermore, I show how such positions can be augmented so as to avoid even these special cases. Doing so requires qualifying the dispositions of interest as those possessed by the abstracted version of an actual agent (in contrast to, say, an idealized version of the agent). In addition to avoiding the finitude problem in its various forms, the position that results provides new materials for appreciating the role that abstracting models can play for a dispositionalist theory of meaning. (shrink)

DP hypothesis of Abney (1987), the syntactic unit that had formerly been known as noun phrase should in fact be analyzed as a phrase headed by a determiner, hence the label DP. Quite independently of this syntactic development, Partee (1987) proposed a type shifting paradigm for the semantic analysis of nominals (now called DPs). In Partee's proposal DPs are ambiguous between a referential reading of type e, a predicative reading of type et and a quantificational reading of type (et)t. DP (...) meanings can flexibly move between their different readings due to covert application of semantic operators. The present paper proposes some strong relationships between these syntactic and semantic paradigms. It is argued that the structure of the DP affects its semantics in that the NP level within the DP is purely predicative and the DP level itself is purely quantificational. However, the intermediate D' level is flexible between the predicate/quantifier semantic categories, due to the covert application of semantic operators at this level. Partee's assumption, adopted from Discourse Representation Theory and more traditional approaches in philosophical logic, that some DPs need to have a (discourse) referential reading, is withdrawn. Instead of Partee's type shifting operators between the three semantic categories she assumes, two operators are used between predicates and quantifiers. The choice function operation of Reinhart (1997) and Winter (1997) is used as a general operator from predicates to quantifiers. The minimum operator of Winter (1996) is used as a general operator from quantifiers to predicates. These two operations, referred to as category shifting operators , account for most of the Partee data and substantially extend the theory of flexibility to treat some intricate phenomena in the domains of coordination, plurality and scope. (shrink)

All accounts of language acquisition agree that, by around age 4, children’s knowledge of grammatical constructions is abstract, rather than tied solely to individual lexical items. The aim of the present research was to investigate, focusing on the passive, whether children’s and adults’ performance is additionally semantically constrained, varying according to the distance between the semantics of the verb and those of the construction. In a forced‐choice pointing study (Experiment 1), both 4‐ to 6‐year olds (N = 60) (...) and adults (N = 60) showed support for the prediction of this semantic construction prototype account of an interaction such that the observed disadvantage for passives as compared to actives (i.e., fewer correct points/longer reaction time) was greater for experiencer‐theme verbs than for agent‐patient and theme‐experiencer verbs (e.g., Bob was seen/hit/frightened by Wendy). Similarly, in a production/priming study (Experiment 2), both 4‐ to 6‐year olds (N = 60) and adults (N = 60) produced fewer passives for experiencer‐theme verbs than for agent‐patient/theme‐experiencer verbs. We conclude that these findings are difficult to explain under accounts based on the notion of A(rgument) movement or of a monostratal, semantics‐free, level of syntax, and instead necessitate some form of semantic construction prototype account. (shrink)

In “Is semantics possible?” Putnam connected two themes: the very possibility of semantics (as opposed to formal model theory) for natural languages and the proper semantic treatment of common nouns. Putnam observed that abstract semantic accounts are modeled on formal languages model theory: the substantial contribution is rules for logical connectives (given outside the models), whereas the lexicon (individual constants and predicates) is treated merely schematically by the models. This schematic treatment may be all that is needed (...) for an account of validity in a formal setting, but it does not help to understand how proper and common nouns function in reality (not in models). Putnam then initiated the empirical study of such nouns to indicate, (i), that the popular Frege-Carnap account of them as (“disguised” compound) predicates is empirically incorrect, and, (ii), that they offer a new paradigm for a naturalistic semantics of natural languages. We take Putnam’s program a couple of steps further. First, we investigate the semantics of common nouns and argue that they refer (to kinds), rather than apply by satisfaction/truth to a designation/denotation. Second, we point to general results about semantics as a theory whose fulcrum is the reference relation rather than satisfaction in models and validity across them. (shrink)

Volume 27, Issue 1, March 2020, Page 89-92.

Argumentation is a very fertile area of research in Artificial Intelligence, and various semantics have been developed to predict when an argument can be accepted, depending on the abstract structure of its defeaters and defenders. When these semantics make conflicting predictions, theoretical arbitration typically relies on ad hoc examples and normative intuition about what prediction ought to be the correct one. We advocate a complementary, descriptive-experimental method, based on the collection of behavioral data about the way human (...) reasoners handle these critical cases. We report two studies applying this method to the case of reinstatement (both in its simple and floating forms). Results speak for the cognitive plausibility of reinstatement and yet show that it does not yield the full expected recovery of the attacked argument. Furthermore, results show that floating reinstatement yields comparable effects to that of simple reinstatement, thus arguing in favor of preferred argumentation semantics, rather than grounded argumentation semantics. Besides their theoretical value for validating and inspiring argumentation semantics, these results have applied value for developing artificial agents meant to argue with human users. (shrink)

Think of a number, any number, or properties like fragility and humanity. These and other abstract entities are radically different from concrete entities like electrons and elbows. While concrete entities are located in space and time, have causes and effects, and are known through empirical means, abstract entities like meanings and possibilities are remarkably different. They seem to be immutable and imperceptible and to exist "outside" of space and time. This book provides a comprehensive critical assessment of the (...) problems raised by abstract entities and the debates about existence, truth, and knowledge that surround them. It sets out the key issues that inform the metaphysical disagreement between platonists who accept abstract entities and nominalists who deny abstract entities exist. Beginning with the essentials of the platonist–nominalist debate, it explores the key arguments and issues informing the contemporary debate over abstract reality: arguments for platonism and their connections to semantics, science, and metaphysical explanation the abstract–concrete distinction and views about the nature of abstract reality epistemological puzzles surrounding our knowledge of mathematical entities and other abstract entities. arguments for nominalism premised upon concerns about paradox, parsimony, infinite regresses, underdetermination, and causal isolation nominalist options that seek to dispense with abstract entities. Including chapter summaries, annotated further reading, and a glossary, _Entities_ is essential reading for anyone seeking a clear and authoritative introduction to the problems raised by abstract entities. (shrink)

Semantic information is usually supposed to satisfy the veridicality thesis: p qualifies as semantic information only if p is true. However, what it means for semantic information to be true is often left implicit, with correspondentist interpretations representing the most popular, default option. The article develops an alternative approach, namely a correctness theory of truth (CTT) for semantic information. This is meant as a contribution not only to the philosophy of information but also to the philosophical debate on the nature (...) of truth. After the introduction, in Sect. 2, semantic information is shown to be translatable into propositional semantic information (i). In Sect. 3, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in Sect. 4, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + A]. This completes the reduction of the truth of i to the correctness of A. In Sects. 5 and 6, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates Q by verifying and validating it (in the computer science’s sense of “verification” and “validation”); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of “proxy”) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of “commutation”); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. Sect. 7 provides some further clarifications about CTT, in the light of semantic paradoxes. Section 8 draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. In the course of the article all technical expressions from computer science are explained. (shrink)

Cognition involves physical stimulation, neural coding, mental conception, and conscious perception. Beyond the neural coding of physical stimuli, it is not clear how exactly these component processes constitute cognition. Within mathematical sciences, category theory provides tools such as category, functor, and adjointness, which are indispensable in the explication of the mathematical calculations involved in acquiring mathematical knowledge. More speci cally, functorial semantics, in showing that theories and models can be construed as categories and functors, respectively, and in establishing the (...) adjointness between abstraction (of theories) and interpretation (to obtain models), mathematically accounts for knowing-within-mathematics. Here we show that mathematical knowing recapitulates--in an elementary form--ordinary cognition. The process of going from particulars (physical stimuli) to their concrete models (conscious percepts) via abstract theories (mental concepts) and measured properties (neural coding) is common to both mathematical knowing and ordinary cognition. Our investigation of the similarity between knowing-within-mathematics and knowing-in-general leads us to make a case for the development of the basic science of cognition in terms of the functorial semantics of mathematical knowing. (shrink)

Abstract: Chomsky (1986) has claimed that the prima facie incompatibility between descriptive linguistics and semantic externalism proves that an externalist semantics is impossible. Although it is true that a strong form of externalism does not cohere with descriptive linguistics, sociolinguistic theory can unify the two approaches. The resulting two-level theory reconciles descriptivism, mentalism, and externalism by construing community languages as a function of social identification. This approach allows a fresh look at names and definite descriptions while also responding (...) to Chomsky's (1993, 1995) challenge to articulate an externalist theory of meaning that can be used in the scientific investigation of language. (shrink)

The Abstract Conceptual Feature (ACF) framework predicts that word meaning is represented within a high‐dimensional semantic space bounded by weighted contributions of perceptual, affective, and encyclopedic information. The ACF, like latent semantic analysis, is amenable to distance metrics between any two words. We applied predictions of the ACF framework to abstract words using eyetracking via an adaptation of the classical “visual word paradigm” (VWP). Healthy adults (n = 20) selected the lexical item most related to a probe word (...) in a 4‐item written word array comprising the target and three distractors. The relation between the probe and each of the four words was determined using the semantic distance metrics derived from ACF ratings. Eye movement data indicated that the word that was most semantically related to the probe received more and longer fixations relative to distractors. Importantly, in sets where participants did not provide an overt behavioral response, the fixation rates were nonetheless significantly higher for targets than distractors, closely resembling trials where an expected response was given. Furthermore, ACF ratings which are based on individual words predicted eye fixation metrics of probe‐target similarity at least as well as latent semantic analysis ratings which are based on word co‐occurrence. The results provide further validation of Euclidean distance metrics derived from ACF ratings as a measure of one facet of the semantic relatedness of abstract words and suggest that they represent a reasonable approximation of the organization of abstract conceptual space. The data are also compatible with the broad notion that multiple sources of information (not restricted to sensorimotor and emotion information) shape the organization of abstract concepts. While the adapted “VWP” is potentially a more metacognitive task than the classical visual world paradigm, we argue that it offers potential utility for studying abstract word comprehension. (shrink)

Humans can understand thousands of abstract words, even when they do not have clearly perceivable referents. Recent views highlight an important role of social experience in grounding of abstract concepts and sub-kinds of abstract concepts, but empirical work in this area is still in its early stages. In the present study, a picture-word semantic priming paradigm was employed to investigate the contribution effect of social experience that is provided by real-life pictures to social abstract concepts and (...) emotional abstract concepts. Using a lexical decision task, we examined responses to picture-SA word pairs and picture-EA word pairs in social/emotional semantically related and unrelated conditions. All pairs shared either positive or negative valence. The results showed quicker responses to positive SA and EA words that were preceded by related vs. unrelated prime pictures. Specifically, positive SA words were facilitated by the corresponding social scene pictures, whereas positive EA words were facilitated by pictures depict the corresponding facial expressions and gestures. However, such facilitatory effect was not observed in negative picture-SA/EA word conditions. This pattern of results suggests that a facilitatory effect of social experience on abstract concepts varies with different sub-kinds of abstract concepts, that seems to be limited to positive SA concepts. Overall, our findings confirm the crucial role of social experience for abstract concepts and further suggest that not all abstract concepts can benefit from social experience, at least in the semantic priming. (shrink)

This paper elaborates distinctions between a core and a periphery in the ontological and the conceptual domain associated with natural language. The ontological core-periphery distinction is essential for natural language ontology and is the basis for the central thesis of my 2013 book Abstract Objects and the Semantics of Natural Language, namely that natural language permits reference to abstract objects in its periphery, but not its core.

We present an analysis of the game semantics of general references introduced by Abramsky, Honda and McCusker which exposes the algebraic structure of the model. Using the notion of sequoidal category, we give a coalgebraic definition of the denotational semantics of storage cells of arbitrary type. We identify further conditions on the model which allow an axiomatic presentation of the proof that finite elements of the model are definable by programs, in the style of Abramsky’s Axioms for Definability.

Our manuscript addresses the foundational question of cognitive science: how do we know? Specifically, examination of the mathematics of acquiring mathematical knowledge revealed that knowing-within-mathematics is reflective of knowing-in-general. Based on the correspondence between ordinary cognition (involving physical stimuli, neural sensations, mental concepts, and conscious percepts) and mathematical knowing (involving objective particulars, measured properties, abstract theories, and concrete models), we put forward the functorial semantics of mathematical knowing as a formalization of cognition. Our investigation of the similarity between (...) mathematics and cognition led us to argue against the compartmentalization of scientific knowledge and ordinary cognition, and make a case for the understanding of the basic science of knowing in terms of functorial semantics. Recognizing functorial semantics as an elementary form of cognition can help advance cognitive science the way calculus helped in the advancement of physics. (shrink)