It is argued that the intuitionistic conception of negation as implication of absurdity is inadequate for the proof-theoretic semantic analysis of negative predication and distinctness. Instead, it is suggested to construe negative predication proof-theoretically as subatomic derivation failure, and to define distinctness—understood as a qualified notion—by appeal to negative predication. This proposal is elaborated in terms of intuitionistic bipredicational subatomic natural deduction systems. It is shown that derivations in these systems normalize and that normal (...) derivations have the subexpression (incl. subformula) property. A proof-theoretic semantics for negative predication and distinctness is defined, and an intuitionistic conception of truth based on canonical derivations is proposed. An application to the doctrine of the Trinity, to which negative predication and distinctness are central, illustrates the systems and their proof-theoretic semantics. (shrink)

This paper explores a neglected category of propositions in Arabic logic, propositions with negative predicates (sālibat al-maḥmūl), by addressing two pivotal questions concerning this propositional form: first, whether it is possible to defend it as distinct from metathetic and simple negative propositions and second, whether affirmative instances of these propositions have existential import. The paper argues for the existence of two distinct and conflicting theories of existential import frequently implicit in the views of Arabic logicians: one centered on (...) the copula and the other on the predicate. (shrink)

According to Aristotelian logic, in categorical logic, there are three kinds of judgements (qaḍīyya): affirmative, negative, and metathetic (ma‘dūla). Khūnajī, a famous Muslim logician in the 13th century, introduces a different judgement (or statement) entitled “affirmative judgement with the negative predicate” (mūjiba al-sāliba al-maḥmūl; henceforth, ANP judgement). Although in the Arabic language, formally, ANP judgement is similar to definite negative (sāliba muḥaṣṣala) and also metathetic judgements, the way of its construction is different from both of them and (...) its truth conditions are different from metathetic ones. From a modern logic viewpoint, ANP may indicate equality judgement; however, attributing it to Muslim logicians is questionable, although some of their wordings may implicitly show it. According to Ḥāʾirī, an Iranian contemporary philosopher and logician, the new judgement is supposed to solve some problems, especially logical explanation of the division of modalities into necessity, impossibility, and contingency (imkān khāṣṣ). However, Ṭabāṭabāʾī, another Iranian contemporary philosopher, disagrees with Ḥāʾirī and regards ANP judgement the same as an affirmative metathetic one. In this paper, while examining Ṭabāṭabāʾī’s and Ḥāʾirī’s reasons, by using some insights into modern logic, I will try to strengthen Ṭabāṭabāʾī’s views, although it may be confronted with some questions or deficiencies. (shrink)

Along the same line as that in Ono (Ann Pure Appl Logic 161:246–250, 2009), a proof-theoretic approach to Glivenko theorems is developed here for substructural predicate logics relative not only to classical predicate logic but also to arbitrary involutive substructural predicate logics over intuitionistic linear predicate logic without exponentials QFLe. It is shown that there exists the weakest logic over QFLe among substructural predicate logics for which the Glivenko theorem holds. Negative translations of substructural predicate logics are studied by (...) using the same approach. First, a negative translation, called extended Kuroda translation is introduced. Then a translation result of an arbitrary involutive substructural predicate logics over QFLe is shown, and the existence of the weakest logic is proved among such logics for which the extended Kuroda translation works. They are obtained by a slight modification of the proof of the Glivenko theorem. Relations of our extended Kuroda translation with other standard negative translations will be discussed. Lastly, algebraic aspects of these results will be mentioned briefly. In this way, a clear and comprehensive understanding of Glivenko theorems and negative translations will be obtained from a substructural viewpoint. (shrink)

The representation of Neg-Raising in the grammar is a matter of controversy. I provide evidence for representing Neg-Raising as a kind of presupposition associated with certain predicates by providing a detailed analysis of NPI-licensing in Neg-Raising contexts. Specific features of presupposition projection are used to explain the licensing of strict NPIs under Neg-Raising predicates. Discussion centers around the analysis of a licensing asymmetry noted in Horn (1971, Negative transportation: Unsafe at any speed? In CLS 7 (pp. 120–133)).Having provided this (...) analysis, I go on to discuss its implications for the theory of NPI-licensing more generally. In particular, I discuss how the present proposal reflects on von Fintel’s (1999, Journal of Semantics, 16, 97–148) proposal to use Strawson downward entailment in the statement of NPI-licensing principles. (shrink)

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)

Neg-Raising concerns the phenomenon by which certain negated predicates can give rise to a reading where the negation seems to take scope from an embedded clause. The standard analysis in pragma-semantic terms goes back to Bartsch and has been elaborated in Horn, Gajewski, Romoli, and many others. Recently, this standard approach has been challenged by Collins and Postal, who argue, by providing various novel arguments, that Neg-Raising involves syntactic movement of the negation from the embedded clause into the matrix clause. (...) The syntactic structure of ‘I don’t think you’re right’ would then be like: I do[n’t]i think you’re ti right, and the Neg-Raising reading would result from the interpretation of the lower copy of the negation. In this paper I present three novel arguments against this account. First, following up work by Horn, I show that Collins and Postal, and their reply to Horn, predict that every negated predicate that can license so-called Horn-clauses should receive a Neg-Raising reading, contrary to fact. Second, Collins and Postal adopt various instances of phonological deletion of negative operators—a necessary ingredient for their account—but these instances of phonological deletion cannot be independently motivated. Third, it turns out that for certain constructions, Collins and Postal must also allude to the original Bartschian approach. I further demonstrate that the standard, pragma-semantic approach to Neg-Raising actually explains the grammaticality of Horn-clauses and other phenomena, such as the distribution of negative parentheticals, that were presented by Collins and Postal as arguments in favour of the syntactic approach to Neg-Raising, equally well, if not better, than this syntactic alternative. (shrink)

This article sketches how the debate over divine predications should be informed by the medieval Islamicate tradition. We emphasize the focus not only on the metaphysics and language of divine predications by al-Ghazali, Maimonides, and others, but also on the epistemology of divine predications. In particular, we emphasize the importance of a theory that explains not only what it takes to make a divine predication true, but also whether these predications are knowable. The epistemological element is central, because traditional (...) views of theology aim to avoid theological skepticism, which is the view that, even if there are theological truths, these truths are unknowable. We pursue this point by emphasizing the role of substantives in al-Ghazalı’s theory of divine predicates, and Maimonides’s discussion of negative predications. In closing we apply these lessons to some recent discussions of theological predication. (shrink)

In his table of judgements, Kant added infinity as a third quality. An infinite judgement ‘All S are non-P’ is said to differ from the affirmative ‘All S are P’ because it ascribes a negative predicate; and it differs from the negative ‘No S is P’ because it has a richer content. The present paper puts three interpretations of this surplus content to six tests. Among other things, it is examined whether these interpretations marry up with Kant’s solution (...) to the first antinomy, his conception of analyticity and the principle of complete determination. The unpleasant conclusion is that none of the interpretations can make its mark as the most adequate one. It thus remains unclear what Kant had in mind when positioning infinite judgements besides affirmative and negative ones. (shrink)

This paper is about the phenomenon known as Neg-Raising. All previous analyses of Neg-Raising fall into one of two categories: syntactic and semantic/pragmatic. The syntactic approach derives the unexpected interpretation of Neg-Raising expressions from a Neg movement operation in the syntax while the semantic/pragmatic approach derives it as an inference attributed to an excluded middle associated with Neg-Raising predicates. In this squib, I discuss a collection of novel and known data, which I argue indicate that both a Neg movement operation (...) as well as an excluded middle are necessary to account for the full range of data. I propose that Neg-Raising is an intrinsically semantic/pragmatic phenomenon and that the Neg movement operation is conditioned by the presence of an excluded middle. I offer a generalization that takes a step towards understanding this mysterious dependency. (shrink)

Now in paperback, Jean-Luc Marion's groundbreaking philosophy of human uncertainty. In Negative Certainties, renowned philosopher Jean-Luc Marion challenges some of the most fundamental assumptions we have developed about knowledge: that it is categorical, predicative, and positive. Following Descartes, Kant, and Heidegger, he looks toward our finitude and the limits of our reason. He asks an astonishingly simple—but profoundly provocative—question in order to open up an entirely new way of thinking about knowledge: Isn’t our uncertainty, our finitude, and rational limitations, (...) one of the few things we can be certain about? Marion shows how the assumption of knowledge as positive demands a reductive epistemology that disregards immeasurable or disorderly phenomena. He shows that we have experiences every day that have no identifiable causes or predictable reasons and that these constitute a very real knowledge—a knowledge of the limits of what can be known. Establishing this “negative certainty,” Marion applies it to four aporias, or issues of certain uncertainty: the definition of man; the nature of God; the unconditionality of the gift; and the unpredictability of events. Translated for the first time into English, Negative Certainties is an invigorating work of epistemological inquiry that will take a central place in Marion’s oeuvre. (shrink)

This paper is a continuation of a long line of footnotes to discussions of the ontological argument which began with Ayer, Wisdom, and Broad, and then progressed through Nakhnikian, Salmon, and Kiteley. In this series, one of the major theses proposed by the first trio and queried by the second is that, if existence is indeed a predicate, then all positive existential statements become analytic and all negative existentials self-contradictory. I should like to question this claim from yet another (...) perspective than that of the more recent writers, viz., that of essential predication. Since it is the so-called second version of the proof which is allegedly more cogent, such a perspective is after all much closer to the core of the ontological argument. Though the remarks here are presented only with regard to positive existentials, they are nevertheless applicable to negative existentials, mutatis mutandis, as well. (shrink)

Contemporary orthodoxy affirms that singular terms cannot be predicates and that, therefore, ‘is’ is ambiguous as between predication and identity. Recent attempts to treat names as predicates do not challenge this orthodoxy. The orthodoxy was built into the structure of modern formal logic by Frege. It is defended by arguments which I show to be unsound. I provide a semantical account of atomic sentences which draws upon Mill's account of predication, connotation and denotation. I show that singular terms (...) may be predicates, that it is highly implausible that there is an ‘is’ of identity in natural languages, and that modern formal logic is deficient in that it cannot recognize sentences, including singular existentials, in which singular terms are predicates, or inferences which depend upon the logical role rather than the logical category of expressions. (shrink)

Avicenna’s logical theory of negative judgement can be seen as a systematic development of the insights Aristotle had laid out in the De interpretatione. However, in order to grasp the full extent of his theory one must extend the examination from the logical works to the metaphysical and psychological bases of negative judgement. Avicenna himself often refrains from the explicit treatment of the connections between logic and metaphysics or psychology, or treats them in a rather oblique fashion. Time (...) and again he is satisfied with noting that this or that question is not proper for a logician and should be dealt with in metaphysics or psychology—without bothering to refer his reader to the exact loci. The following is an attempt at a reconstruction of Avicenna’s theory of negative judgement in such a broad fashion. I will begin with his analysis of negative judgement as resulting from an operation of ‘removing’ the predicate term from the subject term. On this basis, I will move on to discuss how he conceives of the relation between negative judgements and affirmative judgements that contain privative or metathetic terms as well as the question of whether negative judgements can be reduced to affirmative ones. Having thus laid out his logical theory of negation, I move on to discuss the underlying metaphysics by looking at the relation between existence and non-existence, and existence and privation. Finally, I will address Avicenna’s scattered psychological remarks on how we can conceive of what does not exist. (shrink)

In Plato's Parmenides we find on the one hand that the One is denied every property , and on the other hand that the One is attributed every property . In the course of the history of Platonism , these assertions - probably meant by Plato as ontological statements of an entirely formal nature - were repeatedly made the starting points of metaphysical speculations. In the Mystical Theology of the Pseudo-Dionysius they became principles of Christian mysticism and negative theology. (...) I shall show that the two assertions can each be interpreted within the ontological framework of ancient and medieval logic in such a manner that it becomes true, and I shall make plausible that they were understood, with regard to their logical core, by pagan and Christian Platonic metaphysicians just as is indicated by that interpretation. The mentioned ontological framework is basically the Boolean algebra of first-order properties. The main points of the interpretation are on the one hand the identification of the One with the maximal element of the algebra of properties, and on the other hand two alternative intuitively prominent mereological definitions of ontic predication. (shrink)

Some things have positive value and some things have negative value. The things with positive value are good and the things with negative value are bad. There are also things in-between that are neither good nor bad, which are neutral. All in all, then, there are three monadic value predicates: “good,” “bad,” and “neutral.”.

Many philosophers have shown sympathy to the thought that reality is fundamentally positive. Julio De Rizzo formulates this idea precisely by means of the notion of grounding, and examines how the resulting thesis fares with respect to three much discussed classes of negative truths, namely that of negative predications, that of negative causal reports, and that of negative existential truths. By shedding light on the issues advocates of the thesis have to deal with, this work shows (...) the positivist account to be a tenable position in metaphysics. (shrink)

This paper presents an analysis of negative polarity items (NPIs) in Hindi. It is noted that NPIs in this language are composed of a (weak) indefinite plus a particle bhii meaning ‘even’. It is argued that the compositional semantics of this combination explains their behavior as NPIs as well as their behavior as free choice (FC) items. I assume that weak Hindi indefinites like ek and koi are to be viewed as a predicate that I call one, a predicate (...) that is true of everything that exists. I further assume that bhii exhibits association with focus with the indefinite, and that this leads to contradictory implicatures in positive contexts. The behavior of these phrases in a variety of syntactic contexts is discussed, including constructions like correlatives. Finally, I provide a comparison with analyses of English any, and discuss the relevance of the analysis presented here for that of any. (shrink)

There have been a variety of arguments over the decades both for and against syntactic Neg Raising. Two recent papers :559–576, 2018; Crowley in Nat Lang Semant 27, 1–17, 2019) focus on the interaction of NR effects with ellipsis. These papers examine similar types of data, but come to opposite conclusion: Jacobson shows that the ellipsis facts provide evidence against syntactic NR, whereas Crowley argues in favor of syntactic NR. The present paper revisits the evidence, showing that the key case (...) in Crowley that he uses to argue for syntactic NR contains a confound, while the broader set of evidence in Jacobson continues to support the non-syntactic account. In addition, I reply here to an argument for syntactic NR due originally to Prince and Smaby and elaborated on by Crowley. The key generalization can be shown to disappear once contexts are carefully controlled for. Moreover, Crowley extends the Prince/Smaby argument to show that no inference-based account of NR can survive, but this conclusion rests on the claim that there are cases where ever is vacuous; I show that this is not the case. I also consider the question—discussed in much previous literature—of why under the syntactic approach to NR the class of predicates allowing NR is limited to just those which easily support an Excluded Middle inference. Crowley attempts to provide a principled explanation, speculating that NR is allowed just in case it is ‘semantically vacuous’. I argue that this proposal is problematic and so the challenge to syntactic approaches remains. Finally, I provide a new argument against syntactic NR which centers on the behavior of guess. (shrink)

Negative properties, like not flying, are controversial. I introduce negative properties, and offer semantic arguments against the inclusion of such properties in ontology. I distinguish predicate negation and sentential negation, and examine the syntactic and semantic behaviour of predicate negation. I contend that predicate negation is identical with sentential negation. If it is not, then we lose a lot of intuitive inferences found in natural languages and make no clear metaphysical gain. Other arguments based on Ockham’s razor are (...) offered. Finally, I address the problem raised by words like “immortal”. These words apparently express negative properties. My views have interesting consequences on the ontological scope of these words. (shrink)

In this paper, I give an analysis of neg-raising inferences as scalar implicatures. The main motivation for this account as opposed to a presupposition-based approach like Gajewski (Linguist Philos 30(3):289–328, 2007) comes from the differences between presuppositions and neg-raising inferences. In response to this issue, Gajewski (2007) argues that neg-raising predicates are soft presuppositional triggers and adopts the account of how their presuppositions arise by Abusch (J Semantics 27(1):1–44, 2010). However, I argue that there is a difference between soft triggers (...) and neg-raising predicates in their behavior in embeddings; a difference that is straightforwardly accounted for in the present approach. Furthermore, by adopting Abusch’s (2010) account of soft triggers, Gajewski (2007) inherits the assumptions of a pragmatic principle of disjunctive closure and of a non-standard interaction between semantics and pragmatics—assumptions that are not needed by the present proposal, which is just based on a regular theory of scalar implicatures. I also show that the arguments that Gajewski (2007) presents in favor of the presuppositional account can be explained also by the scalar implicatures-based approach proposed here. Finally, while the main point of the paper is a comparison with the presuppositional account, I sketch a preliminary comparison with more syntactic approaches to neg-raising. (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)

The aim of the paper is to illuminate some core aspects of Leibniz’s conception of judgement and its place in his conception of the mind. In particular, the paper argues for three claims: First, the act of judgement is at the centre of Leibniz’s conception of the mind in that minds strive at actualising innate knowledge concerning derivative truths, where the actualising involves an act of judgement. Second, Leibniz does not hold a judgement account of predication, but a two-component (...) account that distinguishes between predication and alethic evaluation. Third, Leibniz understands the act of affirmative judgement in terms of establishing active dispositions, i.e. strivings, to make reasons available for future reasoning that aims at answering whether-questions. Correspondingly, he understands the act of negative judgement in terms of establishing dispositions to ban propositions from future reasoning that aims at answering whether-questions. In the final analysis, the acts of affirmative as well as of negative judgement turn out to be acts of changing memory dispositions. (shrink)

We settle a number of questions concerning definability in first order logic with an extra predicate symbol ranging over semi-linear sets. We give new results both on the positive and negative side: we show that in first-order logic one cannot query a semi-linear set as to whether or not it contains a line, or whether or not it contains the line segment between two given points. However, we show that some of these queries become definable if one makes small (...) restrictions on the semi-linear sets considered. (shrink)

Vagueness is understood as the problem of associating imprecise application criteria with ordinary predicates such as ‘bald’ or ‘blue’. It is often construed as due to one’s tolerance to a minute difference in forming a verdict on the application of a vague predicate. This paper reports an experiment conducted to test the effect of tolerance, using as paradigm categorisation tasks performed with respect to transitional series, e.g., a series of tomatoes from red to orange. The findings suggest a negative (...) effect of tolerance on categorisation with vague predicates. The implication of the findings for certain commonly-held assumptions about tolerance is discussed. (shrink)

What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has been endorsed by many authors (cf. van Benthem 1991). We will investigate these fragments, and find that, illuminating and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this (...) claim.) As a counterproposal, then, we define a large fragment of predicate logic characterized by its use of only bounded quantification. This so-called guarded fragment enjoys the above nice properties, including decidability, through an effectively bounded finite model property. (These are new results, obtained by generalizing notions and techniques from modal logic.) Moreover, its own internal finite variable hierarchy turns out to work well. Finally, we shall make another move. The above analogy works both ways. Modal operators are like quantifiers, but quantifiers are also like modal operators. This observation inspires a generalized semantics for first-order predicate logic with accessibility constraints on available assignments (cf. N´emeti 1986, 1992) which moves the earlier quantifier restrictions into the semantics. This provides a fresh look at the landscape of possible predicate logics, including candidates sharing various desirable features with basic modal logic – in particular, its decidability. (shrink)

The completeness w.r.t. Kripke frames with equality (or, equivalently, w.r.t. Kripke sheaves, [ 8 ] or [4, Sect. 3.6]) is established for three superintuitionistic predicate logics: ( Q - H + D *), ( Q - H + D *&K), ( Q - H + D *& K & J ). Here Q - H is intuitionistic predicate logic, J is the principle of the weak excluded middle, K is Kuroda’s axiom, and D * (cf. [ 12 ]) is a (...) weakened version of the well-known constant domains principle D . Namely, the formula D states that any individual has ancestors in earlier worlds, and D * states that any individual has $${\neg\neg}$$ -ancestors (i.e., ancestors up to $${\neg\neg}$$ -equality) in earlier worlds. In particular, the logic ( Q - H + D *& K & J ) is the Kripke sheaf completion of ( Q - H + E & K & J ), where E is a version of Markov’s principle (cf. [ 12 ]). On the other hand, we show that the logic ( Q - H + D *& J ) is incomplete w.r.t. Kripke sheaves. (shrink)

The “dynamic turn” in the field of second language acquisition catalyzed scholarly devotion to the complex dynamic relationships between learner and teacher variables and various academic emotions. As such, the present study examined the varying effects of the aforementioned variables on the constructs of positive and negative flow, and determined their strongest predictors, respectively. This study used a mixed-method approach to collect data from 607 Chinese English-as-a-Foreign-Language learners. In stage one of the research, the researcher first assessed the participants’ (...) levels of positive flow and negative flow in a blended learning context, then performed Pearson correlation analysis to confirm a significant, but weak positive relationship between positive flow and negative flow. Then, significant difference tests were run to determine the varied effects of those variables on flow. Finally, two multiple regression analyses were conducted to identify five predictors of positive flow, with the biggest contribution coming from learners’ attitudes toward the foreign language, and three predictors of negative flow, with the learners’ major accounting for the majority of variance. In the second stage of the research, a qualitative corpus was constructed, based on accounts of classroom experiences from 71 participants of the total sample, and further illustrated the quantitative findings. Pedagogical implications for educational psychologists and teachers of second and/or foreign languages are addressed. (shrink)

This chapter offers a new solution to the paradox of negative emotion in art. Crucial to the defense of this new solution is the normative sense of predicates such as 'is moving', 'is touching', 'is powerful', and 'is gripping'. Roughly, the solution itself is that, in their normative sense, these predicates designate aesthetic properties that we enjoy and value experiencing, even tough, in the cases which generate the paradox, the enjoyment comes at a price.

Sentences containing definite descriptions, expressions of the form ‘The F’, can be formalised using a binary quantifier ι that forms a formula out of two predicates, where ιx[F, G] is read as ‘The F is G’. This is an innovation over the usual formalisation of definite descriptions with a term forming operator. The present paper compares the two approaches. After a brief overview of the system INFι of intuitionist negative free logic extended by such a quantifier, which was presented (...) in (Kürbis 2019), INFι is first compared to a system of Tennant’s and an axiomatic treatment of a term forming ι operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of INFι in which the G of ιx[F, G] is restricted to identity. INFι is then compared to an intuitionist version of a system of Lambert’s which in addition to the term forming operator has an operator for predicate abstraction for indicating scope distinctions. The two systems will be shown to be equivalent through a translation between their respective languages. Advantages of the present approach over the alternatives are indicated in the discussion. (shrink)

The basic principle of all realist theories of truth developed in the 13th and 14th centuries was that a proposition is true if and only if it tells us how things are in reality. Walter Burley (1275-1344) interpreted this principle in a more radical way than 13th-century realists did. Burley, in fact, proposed a strong correspondence theory, in which there is a strict biunique correspondence between linguistic and extra-linguistic elements. Now, if the principle of correspondence can be applied to Burley (...) unconditionally to all affirmative statements (both for accidental and essential predications), it cannot be applied in the case of negative propositions, since in reality there can be no negative state of affairs. In order to solve this problem, Burley uses the strategy of introducing a complex mental object or objective entity as the significatum adequatum of negative sentences. It is an object which, although it exists only in the mind, is completely independent of our mental operations and which ultimately refers to the extra-mental world, composed exclusively of positive objects and states of affairs. In fact, the truth of a negative sentence does not depend on it corresponding to some negative fact, but rather on the opposite affirmative sentence failing to correspond to some positive extramental fact. Thus, extramental reality, which is only composed of positive objects, recovers its role as a yardstick for verifying the truth or falsity of all particular sentences, both affirmative and negative. (shrink)

During the Middle Ages, heterodox applications of crucial tenets of Aristotle’s philosophy led philosophers to explore connections and suggestions that would have not been acceptable for the Stagirite. In this essay, I explore the conflagration of two such Aristotelian (or pseudo-Aristotelian) theses. First, I investigate the notion that prime matter cannot have any properties (as described, among others, by Simplicius and Aquinas); secondly, I take into account the thesis that no property can substantially be predicated of God (John Damascene, Pseudo-Dionysius, (...) Aquinas). In the first half of the article, I reconstruct the tradition surrounding these two tenets and I argue that a non-trivial conflict between these two theses was explored by David of Dinant, in his lost Quaternuli. He claimed that, since both God and prime matter have no properties, then the impossibility of discerning between the two forces us to admit that God is the prime matter of the world, and to identify God as the material cause of the world. In the second part of the essay, I explore whether his association of the Aristotelian denial of prime matter’s properties and the Scholastic denial of the proper predicability of God’s properties is a sound argument, in light of potential objections regarding the homogeneity of the two denials (prima facie, one seems ontological, and the other epistemological), and the tenability of his negative theory of predication. (shrink)

I argue in §1 that there is a clear distinction between predicate negation and sentential negation and that sentential negation is a special case of predicate negation operating on the predicate ‘is true’. In §2 I reply to Richard’s objections to negative properties on the basis of the conception of properties as identity conditions presented in Chapter 12 of Logical Forms.

It is often said that the ontological argument fails because it wrongly treats existence as a first-level property or predicate. This has proved a controversial claim, and efforts to evaluate it are complicated by the fact that the words ‘existence is not a property/predicate’ have been used by philosophers to make at least three different negative claims: (a) one about a first-level phenomenon possessed by objects like horses, stones, you and me; (b) another about the logical form of assertions (...) of existence; and (c) still another about a second-level phenomenon possessed by concepts when they are instantiated. I argue that only the last of these claims, originally voiced by Kant, is both plausible and relevant to the ontological argument. And I try to show that the relevance of the Kantian version comes from its providing the underlying justification for a different, and far less controversial, criticism of the ontological argument. (shrink)

In this paper, I use an example from the history of philosophy to show how independently defining each side of a pair of contrary predicates is apt to lead to contradiction. In the Euthyphro, piety is defined as that which is loved by some of the gods while impiety is defined as that which is hated by some of the gods. Socrates points out that since the gods harbor contrary sentiments, some things are both pious and impious. But “pious” and (...) “impious” are contrary predicates; they cannot simultaneously characterize the same thing. Euthyphro changes his definition, but the problem of recognizing emotional ambivalence is only side-stepped. I go on to show how contemporary philosophers run into a similar problem. According to Prinz, something is good if and only if we harbor positive sentiments towards it and bad if and only if we harbor negative sentiments towards it. Thus, if we are ambivalent towards something (if we harbor both positive and negative sentiments towards it), then it is both good and bad. Like “pious” and “impious”, “good” and “bad” are contraries. Next, according to the fitting-attitude theory first elaborated by Brentano and favored by contemporary meta-ethicists like Blackburn, Brandt, Ewing, Garcia, Gibbard, McDowell, and Wiggins, something is good if and only if it is a fitting (appropriate) object of approbation, and something is bad if and only if it is a fitting (appropriate) object of disapprobation. I argue that moral ambivalence is sometimes appropriate, i.e., that the correct response to some things is to both love and hate them. Hence, according to the fitting-attitudes theory, some things are both good and bad. I conclude by discussing a variety of ways in which the problem of ambivalence may be solved, suggesting that attitudes of approbation and disapprobation be further individuated by the reasons for them. (shrink)

This article questions the place of negative Forms in Plato’s ontology. And it does so against appearances to the contrary, given that Plato himself seems to acknowledge both positive Forms and negative Forms, that is to say, both good ones and bad ones. He may not say so outright, but he invokes both and rejects neither. The apparent finality of this impression is so strong that it creates a lack of direct interest in the subject: Plato scholars do (...) not give negative Forms much thought except where the prospect relates to something else they happen to be doing. Yet when they do give the matter any thought at all, typically for the sake of a prior concern, they try either to support the textual evidence or to contradict it, indicating that the evidence does not stand on its own. The aim of this article is to determine why they tend to affirm or deny the obvious, how they try to confirm or dispute it, and what this says about Plato’s position. The strategic vehicle is a comparative case study. The confirmation comes from Debra Nails (2013), who needs to embrace negative Forms to demonstrate that the unhypothetical first principle of everything is not identical to the Form of the Good, something she cannot do unless Plato recognizes negative Forms. The contradiction comes from Holger Thesleff (2013), who needs to reject negative (Ideal) Forms because the defining feature of his (Ideal) Forms is the possession of positive intrinsic value, which cannot be predicated of anything negative. Despite defending opposite views, or perhaps because of this, they jointly make up for any lack of interest in the scholarly community. I appreciate both yet side with Thesleff. (shrink)

Expressives are words that convey speakers’ attitudes towards a particular object or situation. Consider two examples:Attributive: That f**khead Jeremy forgot the turkey.Predicative: Jeremy is a f**khead. In both examples the word f**khead communicates some expressive content - the negative attitude of the speaker. However, only in Predicative does it appear to contribute to the truth-conditional content. The task is to explain the semantics of the word f**khead when it seemingly behaves wildly differently in different syntactic positions. In this paper (...) I consider several good candidates for dealing with f**khead occurring in Predicative position: Expressivist and Descriptive approaches that treat f**khead in Predicative as purely descriptive; and Expressive-Contextualism that treats Predicative as communicating to both expressive and descriptive dimensions. I show that none of the options fully capture the meaning of f**khead. Treating Predicative as purely descriptive leaves out the highly important expressive element, whilst Contextualist semantics does not seem as a suitable descriptive theory for expressives. I finally present a novel hybrid account that combines Expressivist semantics with Relativism. I call this view Expressive-Relativism. I show that by adopting Expressive-Relativism we can not only explain the relationship of f**khead in Attributive and Predicative, but also give a suitable descriptive theory that captures the truth-conditions of Predicative. (shrink)

We give a simple proof-theoretic argument showing that Glivenko’s theorem for propositional logic and its version for predicate logic follow as an easy consequence of the deduction theorem, which also proves some Glivenko type theorems relating intermediate predicate logics between intuitionistic and classical logic. We consider two schemata, the double negation shift (DNS) and the one consisting of instances of the principle of excluded middle for sentences (REM). We prove that both schemata combined derive classical logic, while each one of (...) them provides a strictly weaker intermediate logic, and neither of them is derivable from the other. We show that over every intermediate logic there exists a maximal intermediate logic for which Glivenko’s theorem holds. We deduce as well a characterization of DNS, as the weakest (with respect to derivability) scheme that added to REM derives classical logic. (shrink)

The traditional Square of Opposition consists of four sentence types. Two are universal and two particular; two are affirmative and two negative. Examples, where ‘S’ and ‘P’ designate the subject and the predicate, are: ‘every S is P’, ‘no S is P’, ‘some S is P’ and ‘some S is not P’. Taking the usual sentences of the square of opposition, quantifying over their predicates exhibits non-standard sentence forms. These sentences may be combined into non-standard Squares of Opposition , (...) and they reveal a new relationship not found in the usual Square. Medieval logicians termed ‘disparatae’ pairs of sentences like ‘every S is some P’ and ‘some S is every P’, which are neither subaltern nor contrary, neither contradictory nor subcontrary. Walter Redmond has designed a special language L to express the logical form of these sentences in a precise way. I will use this language to show how Squares of Opposition, standard and non-standard, form a complex network of relations which bring to .. (shrink)

The Kripke-completeness and incompleteness of some intermediate predicate logics is established. In particular, we obtain a Kripke-incomplete logic (H* +A+D+K) where H* is the intuitionistic predicate calculus, A is a disjunction-free propositional formula, D = x(P(x) V Q) xP(x) V Q, K = ¬¬x(P(x) V ¬P(x)) (the negative answer to a question of T. Shimura).

In this paper we explore how some of the largest US-newspapers linguistically frame immigrants to the USA in articles about Mexican and Central American immigrants. Specifically, it is a corpus-assisted discourse study which examines the frequency of different semantic predicate-types with migrant subjects and migrant by-agents in the quest for underlying positive or negative biases. We wish to ascertain what activities migrants are presented as taking part in, principally as agents. The analysis shows that more than half of the (...) migrant/predicate-pairings reflect the dictionary definitions of migrant. However, immigrants are described as illegal 66% of the times that their location is mentioned with an immigrant/predicate-pairing. The non-definition-confirming pairings also show evidence of a negative framing of immigrants, but not of migrants. Furthermore, immigrants are more often than migrants cast as agents of activities that do not simply reiterate their status as migrants. Finally, we found evidence of the Negation Bias in the immigrant/predicate-pairings. (shrink)

Since Plato’s Symposium, romantic, sexual love has been characterized as a movement in desire that seeks wholeness and identity since it is, at heart, broken.1 The yearning for sexual consummation is predicated upon the idea that love completes the self. Copulation provides lovers with a moment of rapture, relief, and oneness, but once satisfied it is again wanting in reawakening the desire to pledge and to make love again. Love operates much like a promise whose constant and insistent offerings seek (...) to recover again and again its inherent brokenness. The promise of love and the many promises of love are divided further by the dual possibility of being fulfilled or unfulfilled, sincere or insincere, true or false... (shrink)

This book attempts to marry truth-conditional semantics with cognitive linguistics in the church of computational neuroscience. To this end, it examines the truth-conditional meanings of coordinators, quantifiers, and collective predicates as neurophysiological phenomena that are amenable to a neurocomputational analysis. Drawing inspiration from work on visual processing, and especially the simple/complex cell distinction in early vision (V1), we claim that a similar two-layer architecture is sufficient to learn the truth-conditional meanings of the logical coordinators and logical quantifiers. As a prerequisite, (...) much discussion is given over to what a neurologically plausible representation of the meanings of these items would look like. We eventually settle on a representation in terms of correlation, so that, for instance, the semantic input to the universal operators (e.g. and, all)is represented as maximally correlated, while the semantic input to the universal negative operators (e.g. nor, no)is represented as maximally anticorrelated. On the basis this representation, the hypothesis can be offered that the function of the logical operators is to extract an invariant feature from natural situations, that of degree of correlation between parts of the situation. This result sets up an elegant formal analogy to recent models of visual processing, which argue that the function of early vision is to reduce the redundancy inherent in natural images. Computational simulations are designed in which the logical operators are learned by associating their phonological form with some degree of correlation in the inputs, so that the overall function of the system is as a simple kind of pattern recognition. Several learning rules are assayed, especially those of the Hebbian sort, which are the ones with the most neurological support. Learning vector quantization (LVQ) is shown to be a perspicuous and efficient means of learning the patterns that are of interest. We draw a formal parallelism between the initial, competitive layer of LVQ and the simple cell layer in V1, and between the final, linear layer of LVQ and the complex cell layer in V1, in that the initial layers are both selective, while the final layers both generalize. It is also shown how the representations argued for can be used to draw the traditionally-recognized inferences arising from coordination and quantification, and why the inference of subalternacy breaks down for collective predicates. Finally, the analogies between early vision and the logical operators allow us to advance the claim of cognitive linguistics that language is not processed by proprietary algorithms, but rather by algorithms that are general to the entire brain. Thus in the debate between objectivist and experiential metaphysics, this book falls squarely into the camp of the latter. Yet it does so by means of a rigorous formal, mathematical, and neurological exposition – in contradiction of the experiential claim that formal analysis has no place in the understanding of cognition. To make our own counter-claim as explicit as possible, we present a sketch of the LVQ structure in terms of mereotopology, in which the initial layer of the network performs topological operations, while the final layer performs mereological operations. The book is meant to be self-contained, in the sense that it does not assume any prior knowledge of any of the many areas that are touched upon. It therefore contains mini-summaries of biological visual processing, especially the retinocortical and ventral /what?/ parvocellular pathways computational models of neural signaling, and in particular the reduction of the Hodgkin-Huxley equations to the connectionist and integrate-and-fire neurons Hebbian learning rules and the elaboration of learning vector quantization the linguistic pathway in the left hemisphere memory and the hippocampus truth-conditional vs. image-schematic semantics objectivist vs. experiential metaphysics and mereotopology. All of the simulations are implemented in MATLAB, and the code is available from the book’s website. • The discovery of several algorithmic similarities between visison and semantics. • The support of all of this by means of simulations, and the packaging of all of this in a coherent theoretical framework. (shrink)