The absence of grammatical subject and object in Parmenides' "it is/it is not" allows the reading of the verbal forms not as copulas but as names, with no implicit subject nor elided predicate. Once there are two only alternatives, contrary and excluding each other, sustaining that a 'no-name' does not grant knowledge implies identifying its opposite – "it is" – as the only name conducive to knowledge in itself, denouncing the 'inconceivability of a knowledge that does not know. If "it (...) is" is the only [name] "which can be thought/known", and "what is" is the way in which 'thought/knowledge' can be accomplished, there is no need to postulate the existence of 'anything' that is, nor of anything that can be said of "what is". Being the only name which "can be thought of/known", the unifying synthesis of "knowledge, knowing and known" in one infallible cognitive state, it is unthinkable that "what is" does not exist. (shrink)

The characterization of thought as a subject reflection about a given object is expressed by an enunciation of predicative order. The introduction of the possibility of a type of thought that it is not constituted in virtue of this presupposition brings a lot of difficulties, which is responsible for why Lloyd treats this theme as an enigma of Greek philosophy, i.e, non-discursive thinking. Plotinus seems to make a distinction between rational and intellectual thought, taking as a starting point the (...) _sui generis_ definition of a thinking that thinks itself. The intriguing nature of this description, i.e, the self-thinking as non-discursive thought, has raised studies with the primary aim to understand how it works this type of thinking. Then to clarify what does it mean to adopt the non-discursive approach. This paper intends to analyze the cited problem in the light of the “non-predicative” of Santos. The hypothesis is that by applying this concept to the discussion it will contribute to increase clarification on the distinction between reason and Intellect. That exercise will be conducted in majority through the reading of V.3 [49] of Plotinus _Enneads_. The nature of the intellectual thought would be non-predicative and the rational would be predicative. (shrink)

. Three logical squares of predication or quantification, which one can even extend to logical hexagons, will be presented and analyzed. All three squares are based on ideas of the non-traditional theory of predication developed by Sinowjew and Wessel. The authors also designed a non-traditional theory of quantification. It will be shown that this theory is superfluous, since it is based on an obscure difference between two kinds of quantification and one pays a high price for differentiating in this way: (...) losing the definability between the existence- and all-quantifier. Therefore, a combination of non-traditional predication and classical quantification is preferred here. (shrink)

Predicate modal formulas with non-modalized quantifiers (call them Q-formulas) are considered as schemata of arithmetical formulas, where is interpreted as the provability predicate of some fixed correct extension T of arithmetic. A method of constructing 1) non-provable in T and 2) false arithmetical examples for Q-formulas by Kripke-like countermodels of certain type is given. Assuming the means of T to be strong enough to solve the (undecidable) problem of derivability in QGL, the Q-fragment of the predicate version of the logic (...) GL, we prove the recursive enumerability of the sets of Q-formulas all arithmetical examples of which are: 1) T-provable, 2) true. In. particular, the first one is shown to be exactly QGL and the second one to be exactly the Q-fragment of the predicate version of Solovay's logic S. (shrink)

In Book Γ of the Metaphysics Aristotle states and attempts to prove what he calls the basic principle of the science of being as being: the law of non‐contradiction. In this paper I defend an interpretation of his proof, inspired by Elizabeth Anscombe's 1961 essay in ‘Three Philosophers’, though some of its features were remarked on by Lukasiewicz in 1910, according to which Aristotle is proving this principle only for substance predicates, and that it is to be understood as the (...) basic principle of metaphysics rather than of logic. It is the principle that every substance has an essential nature, and if it is of the essential nature of x to be F then it cannot be of the essential nature of x to be not‐F since then x's being F and x's being not‐F would be the same. He puts it by saying that in such a case F and not‐F would ‘signify the same’ for x. Since they do not, x cannot be both. (shrink)

Two connected themes have been at the core of the old perplexity regarding thinking and speaking about non-existent objects. One involves a question of reference. Can we refer to non-existent objects without, thereby, recognizing, in some sense, non-existent entities as objects of reference? The other involves a question about existence. Is existence a property representable by a predicate in a logically adequate symbohsm? It is argued (1) that existence is not to be construed as an attribute represented by a predicate, (...) (2) that nonnaming names introduce problems, not solutions to problems, (3) that purported properties such as self-identical are specious, and (4) that the Russell property is also seen to be specious by our consideration of predication. (shrink)

Two connected themes have been at the core of the old perplexity regarding thinking and speaking about non-existent objects. One involves a question of reference. Can we refer to non-existent objects without, thereby, recognizing, in some sense, non-existent entities as objects of reference? The other involves a question about existence. Is existence a property representable by a predicate in a logically adequate symbohsm? It is argued (1) that existence is not to be construed as an attribute represented by a predicate, (...) (2) that nonnaming names introduce problems, not solutions to problems, (3) that purported properties such as self-identical are specious, and (4) that the Russell property is also seen to be specious by our consideration of predication. (shrink)

Two connected themes have been at the core of the old perplexity regarding thinking and speaking about non-existent objects. One involves a question of reference. Can we refer to non-existent objects without, thereby, recognizing, in some sense, non-existent entities as objects of reference? The other involves a question about existence. Is existence a property representable by a predicate in a logically adequate symbohsm? It is argued (1) that existence is not to be construed as an attribute represented by a predicate, (...) (2) that nonnaming names introduce problems, not solutions to problems, (3) that purported properties such as self-identical are specious, and (4) that the Russell property is also seen to be specious by our consideration of predication. (shrink)

Plural definite descriptions across many languages display two well-known properties. First, they can give rise to so-called non-maximal readings, in the sense that they ‘allow for exceptions’. Second, while they tend to have a quasi-universal quantificational force in affirmative sentences, they tend to be interpreted existentially in the scope of negation. Building on previous works, we offer a theory in which sentences containing plural definite expressions trigger a family of possible interpretations, and where general principles of language use account for (...) their interpretation in various contexts and syntactic environments. Our theory solves a number of problems that these previous works encounter, and has broader empirical coverage in that it offers a precise analysis for sentences that display complex interactions between plural definites, quantifiers and bound variables, as well as for cases involving non-distributive predicates. The resulting proposal is briefly compared with an alternative proposal by Križ, which has similar coverage but is based on a very different architecture and sometimes makes subtly different predictions. (shrink)

In this essay, I deal with the problem of the attribution of psychological predicates to non-human animals. The first section illustrates three research topics where it has become scientifically legitimate to explain the conduct of non-human animals by means of the attribution of psychological predicates. The second section discusses several philosophical objections to the legitimacy of such attributions provided by central thinkers from the last decades. I try to show that these objections —which are related among other questions to the (...) holism of the mental, the indeterminacy of the attributions, and the strangeness of animal concepts— can be alleviated. In the third section, I propose to adopt a literalist view of the attributions in the sense articulated by Figdor. At the same time, I argue that one must draw limits to the conceptual change forwarded by her literalist view, taking into account holistic considerations and the fact that the psychological concepts must retain their core notes. (shrink)

Plural predication is a pervasive part of ordinary language. We can say that some people are fifty in number, are surrounding a building, come from many countries, and are classmates. These predicates can be true of some people without being true of any one of them; they are non-distributive predications. However, the apparatus of modern logic does not allow a place for them. Thomas McKay here explores the enrichment of logic with non-distributive plural predication and quantification. His book will be (...) of great interest to philosophers of language, linguists, metaphysicians, and logicians. (shrink)

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also (...) model other axioms of Church’s intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin’s intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions. (shrink)

Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume’s Principle, the other, with the underlying second-order logic—and (...) investigates how much of Frege’s Theorem goes through in various partially predicative fragments of FA. Theorem 1 shows that almost everything goes through, the most important exception being the axiom that every natural number has a successor. Theorem 2 shows that the Successor Axiom cannot be proved in the theories that are predicative in either dimension. (shrink)

Persian possesses a number of stative complex predicates with _dâshtan_ ‘to have’ that express certain kinds of mental state. I propose that these _possessive experiencer complex predicates_ be given a formal semantic treatment involving possession of a portion of an abstract quality by an individual, as in the analysis of property concept lexemes due to Francez and Koontz-Garboden (Language 91(3):533–563, 2015 ; Natural Language and Linguistic Theory 34:93–106, 2016 ; Semantics and morphosyntactic variation: Qualities and the grammar of property concepts, (...) Oxford University Press, 2017 ). Augmented with an analysis of prepositional phrases introducing the target of the mental state and an approach to gradability in terms of measure functions (Wellwood in Measuring predicates, PhD dissertation, University of Maryland, College Park, 2014 ), the analysis explains various properties of possessive experiencer complex predicates, including the behavior of target phrases, the ability of the non-verbal element to be modified by a range of adjectives, the direct participation of the non-verbal element in comparative constructions, and the ability of degree expressions to modify both the non-verbal element and the VP containing the complex predicate. Theoretically, the analysis ties transitive mental state expressions to the grammar and semantics of property concept sentences, which are expressed via possessive morphosyntax cross-linguistically, and connects with syntactic proposals that independently argue for a universal underlyingly possessive morphosyntax for mental state predicates (Noonan in Case and syntactic geometry, PhD dissertation, McGill University, 1992 ; Hale and Keyser in Prolegomenon to a theory of argument structure, MIT Press, 2002 ). The work here also motivates modifications to Francez and Koontz-Garboden’s original proposal, and opens new questions in the original empirical domain of the analysis of possessive predicating strategies for the expression of property concept sentences. (shrink)

This paper is devoted to the formulation and investigation of a dynamic semantic interpretation of the language of first-order predicate logic. The resulting system, which will be referred to as ‘dynamic predicate logic’, is intended as a first step towards a compositional, non-representational theory of discourse semantics. In the last decade, various theories of discourse semantics have emerged within the paradigm of model-theoretic semantics. A common feature of these theories is a tendency to do away with the principle of compositionality, (...) a principle which, implicitly or explicitly, has dominated semantics since the days of Frege. Therefore the question naturally arises whether non-compositionality is in any way a necessary feature of discourse semantics. Since we subscribe to the interpretation of compositionality as constituting primarily a methodological principle, we consider this to be a methodological rather than an empirical question. As a consequence, the emphasis in the present paper lies on developing an alternative compositional semantics of discourse, which is empirically equivalent to its non-compositional brethren, but which differs from them in a principled methodological way. Hence, no attempts are made to improve on existing theories empirically. Nevertheless, as we indicate in section 5, the development of a compositional alternative may in the end have empirical consequences, too. First of all, it can be argued that the dynamic view on interpretation developed in this paper suggests natural and relatively easy to formulate extensions which enable one to deal with a wider range of phenomena than can be dealt with in existing theories. Moreover, the various approaches to the model-theoretic semantics of discourse that have been developed during the last decade, have constituted a ‘fresh start’ in the sense that much of what had been accomplished before was ignored, at least for a start. Of course, this is a justified strategy if one feels one is trying to develop a radically different approach to recalcitrant problems. However, there comes a time when such new approaches have to be compared with the older one, and when an assessment of the pros and cons of each has to be made. One of the main problems in semantics today, we feel, is that a semantic theory such as Montague grammar, and an approach like Kamp’s discourse representation theory, are hard to compare, let alone that it is possible to unify their insights and results.. (shrink)

In Book 3 of 'On Abstinence from Animal Food', Porphyry is traditionally taken to be arguing in favour of the belief that animals are rational. However, elsewhere in his corpus, he endorses the opposite view, declaring that man differs from other mortal animals because he is rational and they are irrational. Jonathan Barnes offers a way of understanding Porphyry’s logical theory which is intended to make it consistent with the traditional interpretation of 'On Abstinence'. He suggests that the same predicate (...) can be related to different subjects in different ways. Porphyry’s claim that man differs from other mortal animals with respect to the predicate ‘rational’, is best understood to mean that whereas ‘rational’ is specifically predicated of man, it is non-specifically predicated of animals. This explains how they differ from man with respect to this predicate, without failing to be rational. This paper argues that there are reasons for rejecting Barnes’ interpretation. Barnes must maintain, for example, that animals possess the apparently incompatible properties of being specifically irrational and non-specifically rational simultaneously. Since Barnes fails to resolve the conflict, Porphyry’s claims that animals are irrational in his logical works pose a significant problem for the traditional interpretation of 'On Abstinence'. (shrink)

According to the well–known argument, the traditional conception of existence and predication leads to the infamous paradox of non-existence. For instance, the sentence ‘Pegasus does not exist’ commits us to accept that there is something that does not exist. The easy way out is to analyze existence as a second–order concept expressing that there is at least one instance of some first–order concept. In this article, I argue that the traditional conception of existence and predication does not lead to the (...) paradox of non-existence. Negative existentials are not subject-predicate sentences that select existing beings only to deny them the property of existence. Aristotle’s insistence that being is not a genus, i.e. that being is not a predicate of some subject, is pivotal. Furthermore, Aristotle does not have a uniform conception of existence and predication. According to Aristotle, to be is to be an item in the categorical scheme, and consequently, every predication of some being should be analysable as one of the most general types of predication according to the categorical scheme. However, in the conceptual framework of Aristotle’s philosophy, a different problem of non-existence arises. For instance, ‘Pegasus is thought-about’ might commits us to the claim that Pegasus is a being of some kind. I reconstruct Aristotle’s solution as being satisfactory in the light of his understanding of predication and existence. Moreover, I suggest that a similar puzzle leads many contemporary philosophers to an abandonment of the Quinean concept of existence and predication in favour of a more traditional approach. (shrink)

We give an extension of the Jónsson‐Tarski representation theorem for both normal and non‐normal modal algebras so that it preserves countably many infinite meets and joins. In order to extend the Jónsson‐Tarski representation to non‐normal modal algebras we consider neighborhood frames instead of Kripke frames just as Došen's duality theorem for modal algebras, and to deal with infinite meets and joins, we make use of Q‐filters, which were introduced by Rasiowa and Sikorski, instead of prime filters. By means of the (...) extended representation theorem, we show that every predicate modal logic, whether it is normal or non‐normal, has a model defined on a neighborhood frame with constant domains, and we give a completeness theorem for some predicate modal logics with respect to classes of neighborhood frames with constant domains. Similarly, we show a model existence theorem and a completeness theorem for infinitary modal logics which allow conjunctions of countably many formulas. (shrink)

In so-called Kripke-type models, each sentence is assigned either to true or to false at each possible world. In this setting, every possible world has the two-valued Boolean algebra as the set of truth values. Instead, we take a collection of algebras each of which is attached to a world as the set of truth values at the world, and obtain an extended semantics based on the traditional Kripke-type semantics, which we call here the algebraic Kripke semantics. We introduce algebraic (...) Kripke sheaf semantics for super-intuitionistic and modal predicate logics, and discuss some basic properties. We can state the Gödel-McKinsey-Tarski translation theorem within this semantics. Further, we show new results on super-intuitionistic predicate logics. We prove that there exists a continuum of super-intuitionistic predicate logics each of which has both of the disjunction and existence properties and moreover the same propositional fragment as the intuitionistic logic. (shrink)

The present work takes the decease of Horst Wessel as an opportunity to present and honour his work (and that of his group), which has not received the attention it deserves. The focus will be on works which might not be sufficiently well-known. Wessel was, as we aim to show, familiar with the international debate concerning logical and philosophical issues and strived to solve them by considering theories of logical consequence, a non-traditional theory of predication and the theory of logical (...) terms, all of which he developed in joint work with Alexander Sinowjew. Wessel had to significantly refine these theories in order to formulate his criticism towards alternative logics and to apply the theories to a treatment of intensional contexts. He was vehemently opposed to approaches which revised fundamental laws of classical logic. Questions concerning the history of Philosophy are addressed in Wessel’s criticism of the Kantian antinomies of pure reason, in Wessel’s contributions to the problem of universals and his analyses of fatalism, tychism and antifatalism. (shrink)

Kant said that existence is not a predicate and Russell agreed, arguing that a sentence such as ‘The king of France exists’, which seems to attribute existence to the king of France, really has a logical form that is not reflected in the surface structure of the sentence at all. While the surface form of the sentence consists of a subject and a predicate, the underlying logical form, according to Russell, is the formula given in. This formula obviously has no (...) subjectpredicate form and in fact has no single constituent that corresponds to the verb phrase ‘exists’ in the surface sentence. ∃x∀y The importance of Russell’s analysis becomes clear when we consider ‘The king of France does not exist’. If this sentence would attribute non-existence to the king it should entail that there is someone who does not exist, just as ‘Mary doesn’t like bananas’ entails that there is someone who doesn’t like bananas. Thus the idea that all sentences have subject-predicate form has led some philosophers to the view that there are objects that lack existence. This embarrassing position can be avoided once Russell’s analysis is accepted: if ‘The king of France does not exist’ is formalised as the negation of formula, no unwanted consequences follow. (shrink)

The paper addresses issues of predicates of taste, both gustatory and aesthetic in dialogue with Michael Glanzberg. The first part briefly discusses his view of anaphora in the determination of the semantics of such predicates, and attempts a friendly generalization of his strategy. The second part discusses his contextualism about statements of taste, of the form A is Φ, and then proposes a pluralist alternative. The literature normally confronts contextualism and relativism here, but the pluralist proposal introduces further options. First, (...) it distinguishes first-level and second-level, more theoretical, approaches. At the first level it introduces the naïve view option, the naive non-dogmatist experiencer who simply claims that A is Φ and that’s it. On meta-level such an experiencer is simply agnostic about further matters. Then, there is the first-level dogmatist stance, characteristic for people who do sincerely debate the issues, who naively believe they are objectively right. The third option is the tolerant, liberal one: “A is Φ; for me, I mean. How do you find it?” On the meta-level, dogmatic disagreement goes well with value-absolutism, entailing that one of the parties is simply wrong, and with relativism. If one is not dogmatist about taste predicates, one should accept that dogmatist is simply wrong; no faultlessness is present. The liberal stance goes well with contextualism. If one is liberal there is no deep disagreement. So, the idea of faultless disagreement is a myth. But the proposal notes that language is open to all possibilities, there is no single option that is obligatory for all speakers. (shrink)

A new formalism for predicate logic is introduced, with a non-standard method of binding variables, which allows a compositional formalization of certain anaphoric constructions, including donkey sentences and cross-sentential anaphora. A proof system in natural deduction format is provided, and the formalism is compared with other accounts of this type of anaphora, in particular Dynamic Predicate Logic.

A free logic is one in which a singular term can fail to refer to an existent object, for example, `Vulcan' or `5/0'. This essay demonstrates the fruitfulness of a version of this non-classical logic of terms (negative free logic) by showing (1) how it can be used not only to repair a looming inconsistency in Quine's theory of predication, the most influential semantical theory in contemporary philosophical logic, but also (2) how Beeson, Farmer and Feferman, among others, use it (...) to provide a natural foundation for partial functions in programming languages. Vis à vis (2), the question is raised whether the Beeson-Farmer-Feferman approach is adequate to the treatment of partial functions in all programming languages. Gumb and the author say No, and suggest a way of handling the refractory cases by means of positive free logic. Finally, Antonelli's solution of a problem associated with the Gumb-Lambert proposal is mentioned. (shrink)

In the framework of set theory we cannot distinguish between natural and non-natural predicates. To avoid this shortcoming one can use mathematical structures as conceptual spaces such that natural predicates are characterized as structurally nice subsets. In this paper topological and related structures are used for this purpose. We shall discuss several examples taken from conceptual spaces of quantum mechanics (orthoframes), and the geometric logic of refutative and affirmable assertions. In particular we deal with the problem of structurally distinguishing between (...) natural colour predicates and Goodmanian predicates like grue and bleen. Moreover the problem of characterizing natural predicates is reformulated in such a way that its connection with the classical problem of geometric conventionalism becomes manifest. This can be used to shed some new light on Goodman's remarks on the relative entrenchment of predicates as a criterion of projectibility. (shrink)

Philosophers have had difficulty in explaining the difference between disjunctive and non-disjunctive predicates. Purely syntactical criteria are ineffective, and mention of resemblance begs the question. I draw the distinction by reference to relations between borderline cases. The crucial point about the disjoint predicate 'red or green', for example, is that no borderline case of 'red' is a borderline case of 'green'. Other varieties of disjunctive predicates are: inclusively disjunctive (such as 'red or hard'), disconnected (such as 'grue' on the usual (...) definitions), and skew (such as 'grue' on an emended definition). 'Green' is not a disjunctive predicate. Nelson Goodman's new riddle of induction elicits yet another response. (shrink)

The primary purpose of this note is to demonstrate that predicative Frege arithmetic naturally interprets certain weak but non-trivial arithmetical theories. It will take almost as long to explain what this means and why it matters as it will to prove the results.

We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field (with infinitesimals). Our approach was inspired by the work of Whitehead (...) (1919), though our philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)

Throughout his corpus, Augustine grapples with the challenge of how to speak of that which exceeds and resists conceptualization. The one who would speak of God is confronted, it seems, by a double‐bind: either one reduces God's transcendence to the immanence of language and concepts, or one remains silent. Even to call God ‘inexpressible’, he remarks in De doctrina christiana, is to predicate something of God and thus make some claim to comprehension. ‘This battle of words’, he continues, ‘should be (...) avoided by keeping silent’. Augustine thus seems to privilege and apophatic strategy. But this is not his last word on the matter. Indeed upon the heels of this passage he carefully notes: ‘And yet, while nothing really worthy of God can be said about him, he has accepted the homage of human voices, and has wished us to rejoice in praising [laude] him with our words.’ My goal in this essay is to consider Augustine's laudatory strategy of ‘praise’ as a non‐objectifying discourse concerning transcendence which navigates the straits between kataphatic theological positivism and apophatic silence. This will be taken up against the horizon of contemporary discussions of transcendence and phenomenology, particularly in the work of Jacques Derrida and Jean‐Luc Marion. (shrink)

We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field. Our approach was inspired by the work of Whitehead, though our (...) philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)

Throughout his corpus , Augustine grapples with the challenge of how to speak of that which exceeds and resists conceptualization. The one who would speak of God is confronted, it seems, by a double‐bind: either one reduces God's transcendence to the immanence of language and concepts, or one remains silent. Even to call God ‘inexpressible’, he remarks in De doctrina christiana, is to predicate something of God and thus make some claim to comprehension. ‘This battle of words’, he continues, ‘should (...) be avoided by keeping silent’ . Augustine thus seems to privilege and apophatic strategy. But this is not his last word on the matter. Indeed upon the heels of this passage he carefully notes: ‘And yet, while nothing really worthy of God can be said about him, he has accepted the homage of human voices, and has wished us to rejoice in praising [laude] him with our words.’ My goal in this essay is to consider Augustine's laudatory strategy of ‘praise’ as a non‐objectifying discourse concerning transcendence which navigates the straits between kataphatic theological positivism and apophatic silence. This will be taken up against the horizon of contemporary discussions of transcendence and phenomenology, particularly in the work of Jacques Derrida and Jean‐Luc Marion. (shrink)

Leibniz's development of a "calculus universalis" stands and falls with his theory of negation. During the entire period of the elaboration of the algebra of concepts, L1, Leibniz had to struggle hard to grasp the difference between propositional and conceptual negation. Within the framework of syllogistic, this difference seems to disappear because 'Omne A non B' may be taken to be equivalent to ‘Omne A est non-B’. Within the "universal calculus", however, the informal quantifier expression 'omne' is to be dropped. (...) Accordingly, ‘A non est B' expresses only the propositional negation of ‘A est B' and is hence logically weaker than ‘A est non-B'. Besides Leibniz's cardinal error of confusing propositional and conceptual negation the following issues are dealt with in this paper: -"Aristotelian" vs. "Scholastic" Syllogistic; – Metalinguistic theory of the truth-predicate; -Individual-concepts vs. concepts in general. (shrink)

The paper discusses the structure of non-verbal predication, with particular reference to the role of the copula. Differently from the main tenets of contemporary logico-philosophical and linguistic theories, a model of predication is proposed where the verbal component (specifically, tense information) is regarded as central in establishing the syntactic and semantic relation between a predicate and its subject. It is thus possible to recover some of the insights of the pre-Fregean analysis of predication. The proposed solution has a number of (...) significant consequences for the structure to be assigned to non-verbal predication, in particular for the semantics of small clause constituents, where the predication is established without the copula. (shrink)

In this work we extend results from [4], [3] and [2] about propositional calculi with graded modalities to the predicative level. Our semantic is based on Kripke models with a single domain of interpretation for all the worlds. Therefore the axiomatic system will need a suitable generalization of the Barcan formula. We haven't considered semantics with world-relative domains because they don't present any new difficulties with respect to classical case. Our language will have, as in [1], constant and function (...) symbols, but they will have a rigid interpretation. In this instance the terms will be considered rigid designators, that is, their interpretations will be the same in all possible worlds (cfr. [5]). Nevertheless we will not consider languages with identity: in this way we avoid the problems of identity in modal contexts. On the other hand, we think that in that context would arise essentially the same problems which occur in classical predicative modal logic. Finally we will consider only denumerable languages because the extension to non denumerable ones isn't conceptually problematic. (shrink)

I argue for two major claims in this paper. First, I argue that the linguistic evidence best supports a certain form of contextualism about predicates of personal taste (PPTs) like ?fun? and ?tasty?. In particular, I argue that these adjectives are both individual-level predicates (ILPs) and anaphoric implicit argument taking predicates (IATPs). As ILPs, these naturally form generics. As anaphoric IATPs, PPTs show the same dependencies on context and distributional behavior as more familiar anaphoric IATPs, for example, ?local? and ?apply?. (...) Moreover, they are subject to important binding-related phenomena, for example, various kinds of anaphora, binding arguments, and strict-sloppy ambiguities. The latter are particularly problematic for relativism, contextualism's major competitor. I argue that relativism cannot account for these binding facts in a non-ad hoc manner. Second, I argue that disagreement is a predictable feature of dialogues involving PPTs in conjunction with the contextualist semantics defended. Appealing to ?off the shelf? analyses of genericity, I show how disagreement arises in just the cases we would expect, licensing just the kinds of responses we would expect. They also suggest promising explanations, unavailable to relativists, of various otherwise puzzling features of disagreements involving PPTs. (shrink)

Presupposing that most predicates do not correspond directly to genuine relations, I argue that all genuine relations are symmetric. My main argument depends on the premise that there are no brute necessities, interpreted so as to require logical and metaphysical necessity to coincide for sentences composed entirely of logical vocabulary and primitive predicates. Given this premise, any set of purportedly primitive predicates by which one might hope to express the facts about non-symmetric relations order their relata will generate an objectionable (...) multiplication of possibilities. In the final section I give a different argument, based on the weaker premise that brute necessities should not be multiplied without necessity. (shrink)

Here, we present a category ${\mathbf {pEff}}$ which can be considered a predicative variant of Hyland's Effective Topos ${{\mathbf {Eff} }}$ for the following reasons. First, its construction is carried in Feferman’s predicative theory of non-iterative fixpoints ${{\widehat {ID_1}}}$. Second, ${\mathbf {pEff}}$ is a list-arithmetic locally cartesian closed pretopos with a full subcategory ${{\mathbf {pEff}_{set}}}$ of small objects having the same categorical structure which is preserved by the embedding in ${\mathbf {pEff}}$ ; furthermore subobjects in ${{\mathbf {pEff}_{set}}}$ are (...) classified by a non-small object in ${\mathbf {pEff}}$. Third ${\mathbf {pEff}}$ happens to coincide with the exact completion of the lex category defined as a predicative rendering in ${{\widehat {ID_1}}}$ of the subcategory of ${{\mathbf {Eff} }}$ of recursive functions and it validates the Formal Church’s thesis. Hence pEff turns out to be itself a predicative rendering of a full subcategory of ${{\mathbf {Eff} }}$. (shrink)

Huw Price’s neo-pragmatist programme of global expressivism (see Huw Price "Naturalism Without Mirrors" (2011) and "Expressivism, Pragmatism and Representationalism" (2013)) faces a challenge — it is susceptible to the charge that the proposed combination of expressivism with a deflationary account of semantics leads to inconsistency. Expressivists about a particular discourse deny that it is representational. Global expressivists face the threat of inconsistency due to their attempts to generalise this denial to include the discourse of semantics. In this paper, I explicate (...) two meta-semantic presuppositions of this charge. I argue that such an explication enables us to construct a consistent account of global expressivism. The key point is that global expressivists should adopt two truth predicates and treat meta-semantics as non-substantial. I argue that this framework provides us with a better grasp of Price’s response to the problem of inconsistency and enables global expressivists to accommodate the correspondence intuition. (shrink)