Debates about the semantics and pragmatics of predicates of personal taste have largely centered on contextualist and relativist proposals. In this paper, I argue in favor of an alternative, absolutist analysis of PPT. Theorists such as Max Kölbel and Peter Lasersohn have argued that we should dismiss absolutism due to its inability to accommodate the possibility of faultless disagreement involving PPT. My aim in the paper is to show how the absolutist can in fact accommodate this possibility by drawing on (...) an account of faultless disagreement that improves upon a recent proposal due to Karl Schafer. In amending Schafer’s proposal, I put forward an empirically informed view of our beliefs regarding matters of personal taste, as well as an account of our assertions concerning such matters. I also argue that absolutists should take disagreement about these matters to be conative, rather than doxastic, in nature. The anticipated result is an independently compelling account of faultless disagreement about matters of personal taste that fits naturally with absolutism. (shrink)

This is the first in a series of papers on Predicative Algebraic Set Theory, where we lay the necessary groundwork for the subsequent parts, one on realizability [B. van den Berg, I. Moerdijk, Aspects of predicative algebraic set theory II: Realizability, Theoret. Comput. Sci. . Available from: arXiv:0801.2305, 2008], and the other on sheaves [B. van den Berg, I. Moerdijk, Aspects of predicative algebraic set theory III: Sheaf models, 2008 ]. We introduce the notion of a predicative category with small (...) maps and show that it provides a sound and complete semantics for constructive set theories like IZF and CZF. The main technical contribution of this paper is that it shows in detail that such categories can always be conservatively embedded in categories that are exact. These exactness properties play a crucial rôle in showing that predicative categories with small maps contain models of set theory and that they are closed under sheaves and realizability. We will prove the former statement in this paper as well, leaving a proof of the closure properties to the papers on realizability and sheaves as mentioned above. (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)

This paper is divided into two parts. Part I provides a resumé of the evolution of the notion of predicativity. Part II describes our own work on the subject.Part I§1. Conceptions of sets.Statements about sets lie at the heart of most modern attempts to systematize all (or, at least, all known) mathematics. Technical and philosophical discussions concerning such systematizations and the underlying conceptions have thus occupied a considerable portion of the literature on the foundations of mathematics.

In this essay, I argue that for sentences of form “A is B” there isa distinction between identity and “mere” predication to be made, and thatLeśniewski’s Ontology puts us in a better position to make this distinctionthan first-order predicate logic. I also gesture at how Ontology could helpus to decide questions of identity. The nub of the matter seems to be a“primordial” sense of the copula that Ontology has at its basis.

This chapter, which provides a discussion on the phenomenological foundations of predicative structure, first introduces the different steps in Edmund Husserl's argument. It is noted that not all judgements can be equated with a nexus between a conceptual function and an argument. The predicative structure shows the orientation of consciousness towards one or more objects taken as a theme of interest and utterance. The genetic phenomenological perspective posits the question of the origin of predicative judgement within a much larger context. (...) Husserl's account amounts to granting a paradigmatic character to the theory of experience of ultimate individual substrates and to the theory of perceptual judgement. Levinasian phenomenology implies a radical rethinking of the primacy of the predicative apophansis. It is noted that language can never be taken as an independent and autonomous dimension. (shrink)

Constructions having the surface form NP be ADJ enough to VP are examined. It is shown that when ADJ in this construction belongs to a small class of adjectives including lucky or to a larger class including wise, a structural ambiguity appears in the complement of enough which is related to the distinction between implied and non-implied complements made in Karttunen . The underlying syntactic structure of NP be ADJ enough to VP when ADJ is lucky or wise is examined (...) and the ambiguity in the complement of enough is explained through a generalization of syntactic properties of implied complements. The analysis proposed depends crucially on the use of complex semantic features to relate syntactic structures which are not derivable from one another transformationally. Hence it represents a certain innovation in syntactic theory. (shrink)

Neural correlates exist for a basic component of logical formulae, PREDICATE(x). Vision and audition research in primates and humans shows two independent neural pathways; one locates objects in body-centered space, the other attributes properties, such as colour, to objects. In vision these are the dorsal and ventral pathways. In audition, similarly separable “where” and “what” pathways exist. PREDICATE(x) is a schematic representation of the brain's integration of the two processes of delivery by the senses of the location of an arbitrary (...) referent object, mapped in parietal cortex, and analysis of the properties of the referent by perceptual subsystems. The brain computes actions using a few “deictic” variables pointing to objects. Parallels exist between such nonlinguistic variables and linguistic deictic devices. Indexicality and reference have linguistic and nonlinguistic (e.g., visual) versions, sharing the concept of attention. The individual variables of logical formulae are interpreted as corresponding to these mental variables. In computing action, the deictic variables are linked with “semantic” information about the objects, corresponding to logical predicates. Mental scene descriptions are necessary for practical tasks of primates, and preexist language phylogenetically. The type of scene descriptions used by nonhuman primates would be reused for more complex cognitive, ultimately linguistic, purposes. The provision by the brain's sensory/perceptual systems of about four variables for temporary assignment to objects, and the separate processes of perceptual categorization of the objects so identified, constitute a pre-adaptive platform on which an early system for the linguistic description of scenes developed. Key Words: argument; attention; deictic; dorsal; logic; neural; object; predicate; reference; ventral. (shrink)

In this book about metaphysics the author defends a realistic view of universals, characterizing the notion of universal by considering language and logic, the idea of possibility, hierarchies of universals, and causation. He argues that neither language nor logic is a reliable guide to the nature of reality and that basic universals are the fundamental type of universal and are central to causation. All assertions and predications about the natural world are ultimately founded on these basic universals. A distinction is (...) drawn between unified particulars and arbitrary particulars ; unified particulars are the terms of causal relations and thus the real constituents of the world. The world is not made up of events but of unified particulars and basic universals. (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)

. 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)

In this thesis I focus on F. H. Bradley's theory of judgment and his doctrine of predication. My goal is to present an account of Bradley's views which pays special attention to his belief that all logical predication must necessarily fail to accomplish what it sets out to do. All assertion , we are told, attempts to state truth, whole and complete; but, in the end, it must fall short. All judgment, Bradley claims, must contain an element of (...) untruth or falsity. And the outcome of this theory of predication is a doctrine of "degrees of truth". No truth is understood as entirely true or entirely false; rather, each has a position in a hierarchy of truths with some being truer than others when measured against the theoretical criterion of absolute knowledge. ;But, this is not to be understood as a sceptical doctrine. I argue that Bradley's doctrine of predicative failure should be seen as the only means by which radical scepticism in the theory of knowledge can be avoided. If we were capable of possessing truths which are whole and complete unto themselves then there would exist no legitimate basis upon which the inferential development of thought could expand beyond a self-enclosed circle. ;In this essay I also examine a persisting historical problem. It is my claim that Bradley's theory should be understood as a continuation of and development within the British neo-Kantian tradition. Bradley's association with this tradition has sometimes been questioned based on scattered statements found in the 1883 edition of the Principles of Logic. Collectively these statements have been referred to as the doctrine of "floating ideas". However, I maintain that the doctrine of floating ideas must be distinguished from the theory of predicative failure . I argue that the two theories should in no way be identified and that certain misinterpretations of Bradley's position have resulted from confusing these two incompatible views. (shrink)

In this paper I investigate Aristotle’s account of predication in Topics I 9. I argue for the following interpretation. In this chapter Aristotle (i) presents two systems of predication cutting across each other, the system of the so-called four ‘predicables’ and of the ten ‘categories’, in order to distinguish them and explore their mutual relationship. I propose a semantic interpretation of the relationship between them. According to this reading, every proposition formed through a predicable constitutes at the same (...) time a predication according to one of the ten categories, and, consequently, signifies one of them, expressing one of the predicative relationship conveyed by them. Further, Aristotle (ii) explains the predicative connection between these two systems and the ten items signified by the ‘things said without any combination’ enumerated in Chapter 4 of the Categories, whose list is almost identical with that of categories in Top. I 9, with the only exception of their first members. (shrink)

Predicates involved in language and reasoning are claimed to radically differ from categories applied to objects. Human predicates are the cognitive result of a contrast between perceived objects. Object recognition alone cannot generate such operations as modification and explicit negation. The mechanism studied by Hurford constitutes at best an evolutionary prerequisite of human predication ability.

Tangled Type Theory was introduced by Randall Holmes in [3] as a new way of approaching the consistency problem for $\mathrm {NF}$. Although the task of finding models for this theory is far from trivial (considering it is equiconsistent with $\mathrm {NF}$ ), ways of constructing models for certain fragments of it have been discovered. In this article, we present a simpler way of constructing models of predicative Tangled Type Theory and consequently of predicative $\mathrm {NF}$. In these new models (...) of predicative $\mathrm {NF}$, the universe is well-orderable and equinumerous to the set of singletons. (shrink)

In the debate between contextualism and relativism about predicates of taste, the challenge from disagreement (the objection that contextualism cannot account for disagreement in ordinary exchanges involving such predicates) has played a central role. This paper investigates one way of answering the challenge consisting on appeal to certain, less focused on, uses of predicates of taste. It argues that the said thread is unsatisfactory, in that it downplays certain exchanges that constitute the core disagreement data. Additionally, several arguments to the (...) effect that the exchanges in question don’t amount to disagreement are considered and rejected. (shrink)

I begin with a kind of phenomenological reporting of the recent war between Israel and the Hezbollah in Lebanon, in order to explain the meaning of the thesis that "historicity is predication" - meaning by that to clarify the sense in which predication is a kind of political act (for good and sufficient philosophical reasons) and how the "objective" description of an evolving war illuminates such a philosophical reading of history.

Lifschitz introduced the notion of defining extensions of predicate default theories not as absolute, but relative to a specified domain. We look specifically at default theories over a countable domain and show the set of default theories which possess an ω -extension is Σ 2 1 -complete. That the set is in Σ 2 1 is shown by writing a nearly circumscriptive formula whose ω -models correspond to the ω -extensions of a given default theory; similarly, Σ 2 1 -hardness (...) is established by a method for translating formulas into default theories in such a way that ω -models of the circumscriptive formula correspond to ω -extensions of the default theory. (shrink)

This paper is concerned with the issue of how predication is possible, as a significant common concern in the philosophy of language, metaphysics and semantics. A ‘subject-comment’ account is suggested in view of its constructive engagement with two relevant competing approaches, i.e., the traditional ‘subject-categorization’ account and the ‘topic-comment’ account. The suggested account views predication as a unifying two-level predication: the primary level of predication is made through recognizing and commenting on some particular attribute(s) of the (...) subject’s semantic referent as a thick object (resulting in a weaker version of Russellian proposition) and the secondary level of predication through categorizing the subject’s semantic referent into a certain group via the Fregean conceptual content of the predicate. (shrink)

Frege's extension of his distinction between Sinn and Bedeutung to predicate terms is widely considered to be problematic. Interpreters generally assume that the notion of Bedeutung comprises the name/bearer relation as a prototype and that the extension is justified only in so far as the relation of predicate terms to their alleged referents is analogous to the relation of names to their bearers. However, interpreters have generally paid insufficient attention to Frege's own dealing with the issue. By examining the relevant (...) passages in Frege's writings, I show that the standard ways of talking about Frege's ascription of Bedeutung to predicates as optional, less evident than the ascription of Sinn, and in need of justification are not in accord with Frege's own conception of predicate reference. There is no textual evidence that the extension takes place for analogical reasons and, in particular, no evidence for the claim that the name/bearer relation is used as a prototype. Frege is visibly not concerned with the relation between predicate terms and their referents, but applies the notion of Bedeutung for reasons of principle. There is indeed the invocation of an analogy, but if we consider the argument in which it occurs it appears that it does not play the justificatory role interpreters attribute to it. In sum, Frege's ascription of Bedeutung to predicates does not imply any mysterious or dubious referentiality of predicate terms. (shrink)

We claim that Kant's doctrine of the "transcendental ideal of pure reason" contains, in an anticipatory sense, a second-order theory of reality (as a second-order property) and of the highest being. Such a theory, as reconstructed in this paper, is a transformation of Kant's metatheoretical regulative and heuristic presuppositions of empirical theories into a hypothetical ontotheology. We show that this metaphysical theory, in distinction to Descartes' and Leibniz's ontotheology, in many aspects resembles Gödel's theoretical conception of the possibility of a (...) supreme being. The proposed second-order modal formalization of the Kantian doctrine of the "transcendental ideal" of the supreme being includes some specific features of Kantian general logic like "categorical", "hypothetical", and exclusive disjunctive propositions as basic forms. (shrink)

As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell's Paradox being derivable in it. This system is, except for minor differences, full second-order logic, augmented by a single non-logical axiom, Frege's Axiom V. It has been known for some time now that the first-order fragment of the theory is consistent. The present paper establishes that both the simple and the ramified predicative second-order fragments are consistent, and that Robinson arithmetic, Q, (...) is relatively interpretable in the simple predicative fragment. The philosophical significance of the result is discussed. (shrink)

The paper analyses the contemporary notion of an extension of apredicate from the perspective of semantics typical for Meinongian logics, andin opposition to the traditional notion of extension. This leads to a discussionof the types of properties that can be predicated about objects as belonging tothe sets of properties ascribed to them, and such that can be predicated aboutthem only ‘externally’. It is also problematic in which sense nonexistentobjects possess the properties ascribed to them. The concluding remarksconcern some issues related (...) to the truth of predications about nonexistentobjects, which is the basic condition to admit them as belonging to theextensions of predicates in the first place. (shrink)

Wajsberg and Jankov provided us with methods of constructing a continuum of logics. However, their methods are not suitable for super-intuitionistic and modal predicate logics. The aim of this paper is to present simple ways of modification of their methods appropriate for such logics. We give some concrete applications as generic examples. Among others, we show that there is a continuum of logics (1) between the intuitionistic predicate logic and the logic of constant domains, (2) between a predicate extension ofS4 (...) andS4 with the Barcan formula. Furthermore, we prove that (3) there is a continuum of predicate logics with equality whose equality-free fragment is just the intuitionistic predicate logic. (shrink)

Fregean predicates applied to Fregean objects are merely defined by a `timeless' deductive order of sentences. They cannot provide sufficient structure in order to explain how names can refer to objects of intuition and how predicates can express properties of substances that change in time. Therefore, the accounts of Wilson and Quine, Prior and Brandom for temporal judgments fail — and a new reconstruction of Kant's transcendental logic, especially of the analogies of experience, is needed.

If the semantic values of predicates are, as Williamson assumes (_Philsophical Perspectives,_ _13_, 505–517, 1999, 509) properties in the intensional sense, then epistemicism is immediate. Epistemicism fails, so also this properties account of predicates. I deploy examination of Williamson’s account as a foil against properties as semantic values, showing that his two positive arguments for bivalence fail, as do his efforts to rescue epistemicism from obvious problems. In Part II I argue that, despite the properties account’s problems, it has an (...) important role to play in compositional semantics. We may separate the problem of how smallest parts of language get attached to the world from the problem of how those parts compose to form complex semantic values. For the latter problem we idealize and treat the smallest semantic values as properties (and referents). So doing functions to put to one side how the smallest parts get worldly attachment, a problem that would just get in the way of understanding composition. Attachment to the world must be studied separately, and I review some of the options. As a bonus we see why the requirement of higher order vagueness is an artifact of taking properties as semantic values literally instead of as a simplifying idealization. (shrink)

Since Aristotle and the Stoa, there has been a clash, worsened by modern predicate logic, between logically defined operator meanings and natural intuitions. Pragmatics has tried to neutralize the clash by an appeal to the Gricean conversational maxims. The present study argues that the pragmatic attempt has been unsuccessful. The “softness” of the Gricean explanation fails to do justice to the robustness of the intuitions concerned, leaving the relation between the principles evoked and the observed facts opaque. Moreover, there are (...) cases where the Gricean maxims fail to apply. A more adequate solution consists in the devising of a sound natural logic, part of the innate cognitive equipment of mankind. This account has proved successful in conjunction with a postulated cognitive mechanism in virtue of which the universe of discourse is stepwise and recursively restricted, so that the negation selects different complements according to the degree of restrictedness of Un. This mechanism explains not only the discrepancies between natural logical intuitions and known logical systems; it also accounts for certain systematic lexicalization gaps in the languages of the world. Finally, it is shown how stepwise restriction of Un produces the ontogenesis of natural predicate logic, while at the same time resolving the intuitive clashes with established logical systems that the Gricean maxims sought to explain. (shrink)

Predication is a central theme in Arabic logic that has undergone significant semantic transformation throughout history. This article explores the evolution of predication's scope and meaning across four successive stages. Rather than pinpointing specific historical moments—given that these transitions lack clearly defined beginnings or endings—the focus is on key propositions that enrich our understanding of predication, drawing on the classifications of thinkers such as Abū Naṣr al-Fārābī (d. 950), Athīr al-Dīn al-Abharī (d. 1262-65), Mullā Ṣadrā (d. 1635), (...) and Muhammad Ḥusayn Ṭabātabāʾī (d. 1981). The transition from the first to the second stage is characterized by the acceptance of natural propositions (ṭabīʿīya), while subsequent stages involve essential primary (dhātī awwalī) and stronger/weaker (ḥaqīqa-raqīqa) propositions. This progression illustrates a shift from expressing the properties of external objects to articulating the properties of concepts, ultimately culminating in the expression of identity between concepts and external entities. The four stages can be summarized as follows: (1) First-order predication; (2) Second-order predication; (3) Second-order identity; (4) First-order identity. (shrink)

Taking the semantic values of predicates to be precise properties leaves no room for predicate vagueness. I suggest instead understanding talk of properties as used in semantics as idealized placeholders for the imprecise results of navigating the word/world interface. Basic predications result by applying imprecise informal rules of word use, and it is in the imprecision of these rules that vagueness arises. The idealized property-placeholders then function to separate the messy process of navigating the word/world interface from the exact rules (...) of semantic composition. This scheme applies a methodology of problem separation that is well known in the physical sciences. (shrink)

Predication is a central theme in Arabic logic that has undergone significant semantic transformation throughout history. This article explores the evolution of predication's scope and meaning across four successive stages. Rather than pinpointing specific historical moments—given that these transitions lack clearly defined beginnings or endings—the focus is on key propositions that enrich our understanding of predication, drawing on the classifications of thinkers such as Abū Naṣr al-Fārābī (d. 950), Athīr al-Dīn al-Abharī (d. 1262-65), Mullā Ṣadrā (d. 1635), (...) and Muhammad Ḥusayn Ṭabātabāʾī (d. 1981). The transition from the first to the second stage is characterized by the acceptance of natural propositions (ṭabīʿīya), while subsequent stages involve essential primary (dhātī awwalī) and stronger/weaker (ḥaqīqa-raqīqa) propositions. This progression illustrates a shift from expressing the properties of external objects to articulating the properties of concepts, ultimately culminating in the expression of identity between concepts and external entities. The four stages can be summarized as follows: (1) First-order predication; (2) Second-order predication; (3) Second-order identity; (4) First-order identity. (shrink)

• The transitive closure of R is the smallest relation S for which: –R⊆S, – S is transitive. • To express ^r one would need an ‘infinite formula’: {(x, y) | R(x, y) ∨ ∃z(R(x, z) ∧ R(z, y)) ∨∃z, v(R(x, z) ∧ R(z, v) ∧ R(v, y)) ∨∃z, v, w(R(x, z) ∧ R(z, v) ∧ R(v, w) ∧ R(w, y)) ∨ · · ·.

The paper contends that the heart of Aristotle's theory of justice is the desert-based principle of proportional equality schematically described in the _Nicomachean Ethics and applied to the organization of the state in the _Politics. It argues against the view that for Aristotle distributive justice is only a means to promoting the common good (Thomas Hurka's maximizing perfectionism interpretation of the _Politics) and against the view of Martha Nussbaum that Aristotle understands the common good in a special way that leads (...) to egalitarian conclusions. (shrink)

The objective of the paper is to analyse the relationship between logic and metaphysics on the basis of predication. Its further aim is to analyse the theory of predication, especially from the perspective of three significant problems: the problem of basic statements, the relationship between subject and predicate, and the analysis of individuals and universals. Another aim of the contribution is to examine the terms such as basic statement, subject, predicate, individuals, universals, and to compare two Russell’s periods, (...) in which his attitudes were different. The last aim of the paper is to find answer to the questions, such as: Can individuals appear in discourse only as subjects, or also as predicates? Can universals exist in both these roles, as subjects and as predicates as well? In other words, which term can we use as subject and which one as a predicate? (shrink)

The nexus of predication is accounted for in different ways in different theories of universals. We briefly review the account given in nominalism, logical realism , and natural realism. Our main goal is to describe the account given in a modern form of conceptualism extended to include a theory of intensional objects as the contents of our predicable and referential concepts.

1.1 There are those who complain that discussions of ‘moral goodness’ neglect the topic of virtue. We have no reason to quarrel with this, as a statement of fact. As a complaint, however, we can find fault with it. And do. There are substantial reasons for virtue’s disappearance from the agenda of ethical discourse. Nevertheless, we shall find cause for continuing our use of the term, but without some of its accumulated baggage.

Bioassessment is the process of using living organisms to assess the ecological health of a particular ecosystem. It typically relies on identifying specific organisms that are sensitive to changes in environmental conditions. Benthic macroinvertebrates are widely used for examining the ecological status of freshwaters. However, a time-consuming process of species identification that requires high expertise represents one of the key obstacles to more precise bioassessment of aquatic ecosystems. Partial automation of this process using deep learning-based image classification is the goal (...) of an ongoing project AIAQUAMI we are participating in. One of the project goals is to develop software support for image classification with visualization and reporting. For that purpose, we developed desktop and web applications that we open-sourced as Imagelytics Suite. Both desktop and web applications rely on a convolutional neural network (CNN) to classify images and the Grad-CAM algorithm to produce heatmaps of the image areas that mostly influenced the network decision. Along with the source code of the applications, we also open-sourced scripts that can be used to train CNN on an arbitrary dataset and produce required metadata, so it can be used with Imagelytics applications. In this article, we presented technical details regarding the design of the applications and the training method that will enable their general use for image classification tasks. As a part of the evaluation, we will show a use case related to species identification of non-biting midges (Diptera: Chironomidae). (shrink)

Immanent realism is a justly popular theory of universals which is incomplete. It is not good enough to say that all universals are equally real and all equally inhere in objects. Concepts come in hierarchies, For example: "colored," "red" and "claret," where "claret" is a shade of red. Only those at the very bottom of the hierarchy exist in objects, And are rightly called properties. Only properties have causality as a criterion of identity. Frege's functional account of concepts can be (...) adapted to explain how higher level concepts apply to objects. Between two concepts at different levels there is a relationship called 'essential subordination', Which is different from all other relationships. That a person is said to possess a concept of a property is to be explained in terms of a person possessing certain mental capacity, Which enables him to make certain judgments. Properties are concepts which exist in objects. (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)

In this article, we present the positional logic that is suitable for the formalization of reasoning about social phenomena. It is the effect of extending the Minimal Realisation (MR) logic with new expressions. These expressions allow, inter alia, to consider different points of view of social entities (humanistic coefficient). In the article, we perform a metalogical analysis of this logic. Finally, we present some simple examples of its application.

Although in every inductive inference, an act of invention is requisite, the act soon slips out of notice. Although we bind together facts by superinducing upon them a new Conception, this Conception, once introduced and applied, is looked upon as inseparably connected with the facts, and necessarily implied in them. Having once had the phenomena bound together in their minds in virtue of the Conception men can no longer easily restore them back to the detached and incoherent condition in which (...) they were before they were thus combined. The pearls once strung, they seem to form a chain by their nature. Induction has given them unity which it is so far from costing us an effort to preserve, that it requires an effort to imagine it dissolved — William Whewell, 1858. (Quoted from Butts (ed.), 1989, p. 143). (shrink)

We give a syntactic translation from first-order intuitionistic predicate logic into second-order intuitionistic propositional logic IPC2. The translation covers the full set of logical connectives ∧, ∨, →, ⊥, ∀, and ∃, extending our previous work, which studied the significantly simpler case of the universal-implicational fragment of predicate logic. As corollaries of our approach, we obtain simple proofs of nondefinability of ∃ from the propositional connectives and nondefinability of ∀ from ∃ in the second-order intuitionistic propositional logic. We also show (...) that the ∀-free fragment of IPC2 is undecidable. (shrink)

Bäck’s thesis is that Aristotle accepts what Bäck calls the aspect theory of predication: the theory that all well-formed affirmative statements in the present tense assert that their subjects now exist. “Fido is brown” means that Fido exists brownly. Thus Aristotle’s copula is really a certain sort of use of the “is” of existence.. On Bäck’s view Aristotle’s ten categories, or “ways in which being is said,” turn out to be ten kinds of way for a subject to exist.

Are there universal properties grounding our sense of resemblance or qualitative identity among a number of distinct things or events which appear to form a class, a type or a kind of some other sort? Do universals such as humanness, triangularity, or being an Oak exist? Is being a laptop computer a universal, which has only recently come into existence? Do predicate expressions, adjectives or abstract nouns refer to objective properties or cognitive contents called concepts? The problem of universals has (...) been at the centre of ancient, medieval, Western, and Indian metaphysics. After the logico-linguistic turn in philosophy, this problem re-surfaced in the discourse on the meaning of predicate expressions on the one hand and in the theories of concepts on the other. (shrink)

In the past four or five years I have been especially dependent on Aristotle's writings as I have initiated a series of experiments that can legitimately be called empirical efforts to prove Aristotelian conceptions to be true. In actuality, of course, I am trying to prove my own theory to be true—that is, worthy of consideration because it is consistent with observed human actions. However, by extension, I am surely seeking evidence for Aristotle's image of human cognition. There are two (...) Aristotlelian conceptions that underwrite my theoretical and empirical efforts: predication and opposition. When we speak of a "predication" in cognition we refer to a process that is fundamentally creative. Predications deal in meanings; and the way in which we align meanings, lending the meaning of one concept to another is what predication is all about. Predication is the act of affirming, denying, or qualifying certain patterns of meaning in relation to other patterns of meaning. The second Aristotelian conception that I have been employing theoretically and investigating empirically is "opposition." Although association through frequent contact was recognized by Aristotle , he also appreciated that there is often an intrinsic tie of opposite meanings to be seen in human reason. In my own interpretation of Aristotle, I believe that we can see the ultimate necessity of predication stemming from the opositional ties of meanings like this. If I am cognizing within a congerie of interlacing meanings which relate to and, indeed, delimit the definitions of their opposite meanings, then it is up to me as a cognizer to continually "take a position" on just what I am going to affirm—or not! 2012 APA, all rights reserved). (shrink)

Anyone with more than casual interest in Aristotle's Categories knows the convention that "predicated of" ["κατηγορεἳται"] marks a general relation of predication while "said of" ["λέγεται"] is reserved for essential predication. By "convention" I simply mean to underscore that the view in question ranks as the conventional or received interpretation. Ackrill, for example, follows the received view in holding that only items within the same category (not arbitrarily, of course) can stand in the being-said-of relation and, thus, that (...) only secondary substances can be said of primary substances. Despite its long received status the convention has never received a fully comprehensive examination and defense. In fact such an account is needed because, while enjoying considerable textual support, certain passages of the Categories appear to clash with the convention. My aim in this paper is, first, to develop and defend the standard interpretation, as I shall call it. Since the standard interpretation has lately been challenged in a closely argued article by Russell Dancy, my defense will proceed partly with an eye to his criticisms. Having met these, I go on to raise some difficulties with the rather unorthodox reading Dancy gives the Categories. The crucial point here turns out to be what Aristotle understands by a paronym. (shrink)

Båve has argued that act-type theories of propositions entail unwanted ambiguity of sentences such as ‘Donald loves Joan’. King has argued that act-type theories of propositions entail an unwanted abundance of propositions. I reply that a version of the act-type theory can avoid these objections. The key idea is that grammar constrains the acts that can be performed by the utterance of a sentence. I present enough of the details of this version of the act-type theory to show how it (...) can be used to respond to Båve's and King's objections. I conclude that this is a promising way to develop the act-type theory of propositions. (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)

The subject of this rich and wide-ranging book is old-fashioned metaphysics: its aim is to give an account of "the real constituents of the world". But its idiom and methodology are those of late twentieth-century analytic philosophy. Newman works out his own positions in constant dialogue with such philosophers as Frege and Wittgenstein, Geach and D. M. Armstrong, Keith Campbell and David Lewis; and he has an impressive mastery of modern formal logic and contemporary philosophy of language. He also makes (...) effective use of a quite detailed understanding of recent work in mathematics and physics. For all his reliance on the concepts and techniques of logic and philosophy of language, however, Newman does not believe that either language or logic "is a reliable guide to the nature of reality". On his view, metaphysics is an autonomous intellectual discipline, at least some of whose convictions and concepts are primitive. (shrink)

An ω-model (a model in which all natural numbers are standard) of the predicative fragment of Quine's set theory "New Foundations" (NF) is constructed. Marcel Crabbe has shown that a theory NFI extending predicative NF is consistent, and the model constructed is actually a model of NFI as well. The construction follows the construction of ω-models of NFU (NF with urelements) by R. B. Jensen, and, like the construction of Jensen for NFU, it can be used to construct α-models for (...) any ordinal α. The construction proceeds via a model of a type theory of a peculiar kind; we first discuss such "tangled type theories" in general, exhibiting a "tangled type theory" (and also an extension of Zermelo set theory with Δ 0 comprehension) which is equiconsistent with NF (for which the consistency problem seems no easier than the corresponding problem for NF (still open)), and pointing out that "tangled type theory with urelements" has a quite natural interpretation, which seems to provide an explanation for the more natural behaviour of NFU relative to the other set theories of this kind, and can be seen anachronistically as underlying Jensen's consistency proof for NFU. (shrink)