In Writing the Book of the World, Ted Sider argues that David Lewis’s distinction between those predicates which are ‘perfectly natural’ and those which are not can be extended so that it applies to words of all semantic types. Just as there are perfectly natural predicates, there may be perfectly natural connectives, operators, singular terms and so on. According to Sider, one of our goals as metaphysicians should be to identify the perfectly natural words. Sider claims that there is a (...) perfectly natural first-order quantifier. I argue that this claim is not justified. Quine has shown that we can dispense with first-order quantifiers, by using a family of ‘predicate functors’ instead. I argue that we have no reason to think that it is the first-order quantifiers, rather than Quine’s predicate functors, which are perfectly natural. The discussion of quantification is used to provide some motivation for a general scepticism about Sider’s project. Shamik Dasgupta’s ‘generalism’ and Jason Turner’s critique of ‘ontological nihilism’ are also discussed. (shrink)

When are logical theories equivalent? I discuss the notion of ground-equivalence between logical theories, which can be useful for various theoretical reasons, e.g., we expect ground-equivalent theories to have the same ontological bearing. I consider whether intertranslatability is an adequate criterion for ground-equivalence. Jason Turner recently offered an argument that first-order logic and predicate functor logic are ground-equivalent in virtue of their intertranslatability. I examine his argument and show that this can be generalized to other intertranslatable logical theories, which (...) supports the following: intertranslatability implies ground-equivalence. I also argue, however, that this ground-equivalence argument can be challenged as it faces a dilemma. The dilemma arises because the argument allows two distinct readings, the ‘internal’ and the ‘external’ reading. I argue that the argument turns out to be unsuccessful in both readings. The upshot of this dilemma in both philosophy of logic and metaphysics is considered. (shrink)

The book is a collection of papers addressing the role of logic in forming and developing philosophy. In particular, on the ground of modern development of logic, it is shown that philosophy can be established (and, in fact, to a large extent is established) as a modern science. The following problems are addressed: general relationship between philosophy and science (especially from a logical viewpoint); the use of logic in ordinary language; names and descriptions; Quine's pragmatic extensional Platonism and predicate-functor (...) logic; philosophical and logical aspects of Gödel's onto-theological system. In the last two chapters, an early critique and emendement of algebraic logic by Croatian philosophers Franjo Marković and Mate Meršić, respectively, is examined. (shrink)

By pure calculus of names we mean a quantifier-free theory, based on the classical propositional calculus, which defines predicates known from Aristotle’s syllogistic and Leśniewski’s Ontology. For a large fragment of the theory decision procedures, defined by a combination of simple syntactic operations and models in two-membered domains, can be used. We compare the system which employs `ε’ as the only specific term with the system enriched with functors of Syllogistic. In the former, we do not need an empty (...) name in the model, so we are able to construct a 3-valued matrix, while for the latter, for which an empty name is necessary, the respective matrices are 4-valued. (shrink)

Predicativity is a notable example of fruitful interaction between philosophy and mathematical logic. It originated at the beginning of the 20th century from methodological and philosophical reflections on a changing concept of set. A clarification of this notion has prompted the development of fundamental new technical instruments, from Russell's type theory to an important chapter in proof theory, which saw the decisive involvement of Kreisel, Feferman and Schütte. The technical outcomes of predica-tivity have since taken a life of their own, (...) but have also produced a deeper understanding of the notion of predicativity, therefore witnessing the " light logic throws on problems in the foundations of mathematics. " (Feferman 1998, p. vii) Predicativity has been at the center of a considerable part of Feferman's work: over the years he has explored alternative ways of explicating and analyzing this notion and has shown that predicative mathematics extends much further than expected within ordinary mathematics. The aim of this note is to outline the principal features of predicativity, from its original motivations at the start of the past century to its logical analysis in the 1950-60's. The hope is to convey why predicativity is a fascinating subject, which has attracted Feferman's attention over the years. (shrink)

Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunctions being the primary lens. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunctions have been hampered by an overly restrictive formulation that avoids heteromorphisms or hets. By reformulating an adjunction using hets, it is split into two parts, a left and a right semiadjunction. Semiadjunctions (...) (essentially a formulation of universal mapping properties using hets) can then be combined in a new way to define the notion of a brain functor that provides an abstract model of the intentionality of perception and action (as opposed to the passive reception of sense-data or the reflex generation of behavior). (shrink)

There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms that parses an adjunction into two separate parts. Then these separate parts can be recombined in a new way to define a cognate concept, the brain functor, to abstractly model the functions of perception and action of a brain. The treatment uses relatively simple category theory (...) and is focused on the interpretation and application of the mathematical concepts. (shrink)

According to indexical contextualism, the perspectival element of taste predicates and epistemic modals is part of the content expressed. According to nonindexicalism, the perspectival element must be conceived as a parameter in the circumstance of evaluation, which engenders “thin” or perspective-neutral semantic contents. Echoing Evans, thin contents have frequently been criticized. It is doubtful whether such coarse-grained quasi-propositions can do any meaningful work as objects of propositional attitudes. In this paper, I assess recent responses by Recanati, Kölbel, Lasersohn and MacFarlane (...) to the “incompleteness worry”. None of them manages to convince. Particular attention is devoted to an argument by John MacFarlane, which states that if perspectives must be part of the content, so must worlds, which would make intuitively contingent propositions necessary. I demonstrate that this attempt to defend thin content views such as nonindexical contextualism and relativism conflates two distinct notions of necessity, and that radical indexicalist accounts of semantics, such as Schaffer’s necessitarianism, are in fact quite plausible. (shrink)

In “Value Ascriptions: Rethinking Cognitivism,” Sigrún Svavarsdóttir offers a novel account of the semantic function of evaluative predication, according to which such predicates function as “linguistically encoded classificatory devices.” This short paper raises three questions about Svavarsdóttir’s account: how it relates to familiar sorts of projects in and about semantics, how to understand the nature of “linguistic encoding,” and how to understand the significance of the account’s central use of sets.

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are (...) predicates in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (shrink)

According to contextualism, the extension of claims of personal taste is dependent on the context of utterance. According to truth relativism, their extension depends on the context of assessment. On this view, when the tastes of a speaker change, so does the truth value of a previously uttered taste claim, and if it is false, the speaker is required to retract it. Both views make strong empirical assumptions, which are here put to the test for the first time in three (...) experiments with over 740 participants. It turns out that the linguistic behaviour of ordinary English speakers is consistent with contextualist predictions and inconsistent with the predictions of the most widely discussed form of truth relativism advocated by John MacFarlane. (shrink)

In this paper we discuss a phenomenon we call perspectival plurality, which has gone largely unnoticed in the current debate between relativism and contextualism about predicates of personal taste. According to perspectival plurality, the truth value of a sentence containing more than one PPT may depend on more than one perspective. Prima facie, the phenomenon engenders a problem for relativism and can be shaped into an argument in favor of contextualism. We explore the consequences of perspectival plurality in depth and (...) assess several possible responses on behalf of advocates of relativism. (shrink)

In the sentence “Tom sits,” the name distinguishes Tom from anyone else, whereas the predicate assimilates Tom, Theaetetus, and anyone else to whom the predicate applies. The name marks out its bearer and the predicate groups together what it applies to. On that ground, his name is used to trace back Tom, and the predi- cate is used to describe and classify what it applies to. In both cases, the semantic link is a direct link between expressions (...) and particulars. Here, I will explore the workings of predicative names along the direction just hinted at. The analysis of predication has been less central to philosophical investigation than that of referen- tial expressions. Some problems have concerned the unity of the sentence—what makes us understand “The baby cries” as a sentence rather than a list of words? Other problems have been what a predicate was taken to stand for, properties and relations, and the understanding of either at the ontological level. If a predicate refers to a property or a relation, yet predication, which is central to our understand- ing of predicates, applies it to one or more particulars. On the background hinted at, these problems might be differently viewed. (shrink)

Several philosophers have recently appealed to predication in developing their theories of cognitive representation and propositions. One central point of difference between them is whether they take predication to be forceful or neutral and whether they take the most basic cognitive representational act to be judging or entertaining. Both views are supported by powerful reasons and both face problems. Many think that predication must be forceful if it is to explain representation. However, the standard ways of implementing the idea give (...) rise to the Frege-Geach problem. Others think that predication must be neutral, if we’re to avoid the Frege-Geach problem. However, it looks like nothing neutral can explain representation. In this paper I present a third view, one which respects the powerful reasons while avoiding the problems. On this view predication is forceful and can thus explain representation, but the idea is implemented in a novel way, avoiding the Frege-Geach problem. The key is to make sense of the notion of grasping a proposition as an objectual act where the object is a proposition. (shrink)

In this article I present a disagreement between classical and constructive approaches to predicativity regarding the predicative status of so-called generalised inductive definitions. I begin by offering some motivation for an enquiry in the predicative foundations of constructive mathematics, by looking at contemporary work at the intersection between mathematics and computer science. I then review the background notions and spell out the above-mentioned disagreement between classical and constructive approaches to predicativity. Finally, I look at possible ways of defending the constructive (...) predicativity of inductive definitions. (shrink)

This takes a closer look at the actual semantic behavior of apparent truth predicates in English and re-evaluates the way they could motivate particular philosophical views regarding the formal status of 'truth predicates' and their semantics. The paper distinguishes two types of 'truth predicates' and proposes semantic analyses that better reflect the linguistic facts. These analyses match particular independently motivated philosophical views.

I argue against the standard interpretation of Aristotle’s account of ‘natural predication’ in Posterior Analytics 1.19 and 1.22 according to which only substances can serve as subjects in such predications. I argue that this interpretation cannot accommodate a number of demonstrations Aristotle sanctions. I propose a new interpretation that can accommodate them.

A predicate logic typically has a heterogeneous semantic theory. Subjects and predicates have distinct semantic roles: subjects refer; predicates characterize. A sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. Traditional term logic, by contrast, has a homogeneous theory: both subjects and predicates refer; and a sentence is true if the subject and predicate name one and the same thing. In this paper, I will examine evidence for ascribing (...) to Aristotle the view that subjects and predicates refer. If this is correct, then it seems that Aristotle, like the traditional term logician, problematically conflates predication and identity claims. I will argue that we can ascribe to Aristotle the view that both subjects and predicates refer, while holding that he would deny that a sentence is true just in case the subject and predicate name one and the same thing. In particular, I will argue that Aristotle's core semantic notion is not identity but the weaker relation of constitution. For example, the predication ‘All men are mortal’ expresses a true thought, in Aristotle's view, just in case the mereological sum of humans is a part of the mereological sum of mortals. (shrink)

Natural languages generally distinguishes among different existence predicates for different types of entities, such as English 'exist', 'occur', and 'obtain'. The paper gives an in-depth discussion and analysis of a range of existence predicates in natural language within the general project of descriptive metaphysics, or more specifically ‘natural language ontology’.

Simple sentences containing predicates like "tasty" and "beautiful" typically suggest that the speaker has first-hand knowledge of the item being evaluated. I consider two explanations of this acquaintance inference: a presuppositional approach and a pragmatic-epistemic approach. The presuppositional approach has a number of virtues, but runs into trouble because the acquaintance inference has a very different projection pattern from that of standard presuppositions. The pragmatic-epistemic approach accounts for the main data discussed in the paper, but faces challenges of its own.

This chapter compares simple predicates of personal taste (PPTs) such as tasty and beautiful with their complex counterparts (eg tastes good, looks beautiful). I argue that the former differ from the latter along two dimensions. Firstly, simple PPTs are individual-level predicates, whereas complex ones are stage-level. Secondly, covert Experiencer arguments of simple PPTs obligatorily receive a generic interpretation; by contrast, the covert Experiencer of a complex PPT can receive a generic, bound variable or referential interpretation. I provide an analysis of (...) these facts based on a novel proposal about the licensing of individual-level predicates (the ‘Licensing Condition on ILPs’). This condition states that all covert pronominal arguments of an individual-level predicate must be bound by the generic operator. Finally, I show that generic construal of the Experiencer is a necessary condition for faultless disagreement. This is evidence in favour of treatments of subjective meaning that appeal to genericity, and against relativism about PPTs. (shrink)

Over the course of the past ten-plus years, Peter Hanks and Scott Soames have developed detailed versions of Act-Based views of propositions which operate with the notions of reference to objects, indicating properties, predication, and judgment (or entertaining). In this paper I discuss certain foundational aspects of the Act-Based approach having to do with the relations between these notions. In particular, I argue for the following three points. First, that the approach needs both an atomistically understood thin notion of reference, (...) a bare act of thinking of o, as well as a more involved notion, something like making o a target of predication. Second, that the acts of thinking of o and indication of the property of being F are in no sense parts of the acts of predication of being F of o and judgment that o is F. Rather, the former are simply necessary preconditions for the performance of the latter. The acts of predication or judgment are emphatically not structured sequences of separate acts but unities in and of themselves. Finally, that we should understand the Act-Based theorists’ claim that to predicate is to judge as the claim that judgment can be reductively analyzed in terms of predication. Furthermore, while predication is metaphysically a multiple relation between a predicator, a target, and the property predicated, judgment is a monadic property, just one that has propositional content. (shrink)

This paper argues that truth predicates in natural language and their variants, predicates of correctness, satisfaction and validity, do not apply to propositions (not even with 'that'-clauses), but rather to a range of attitudinal and modal objects. As such natural language reflects a notion of truth that is primarily a normative notion of correctness constitutive of representational objects. The paper moreover argues that 'true' is part of a larger class of satisfaction predicates whose semantic differences are best accounted for in (...) terms of a truthmaker theory along the lines of Fine's recent truthmaker semantics. (shrink)

Despite the wide acceptance of standard modal logic, there has always been a temptation to think that ordinary modal discourse may be correctly analyzed and adequately represented in terms of predicates rather than in terms of operators. The aim of the formal model outlined in this paper is to capture what I take to be the only plausible sense in which ‘possible’ and ‘necessary’ can be treated as predicates. The model is built by enriching the language of standard modal logic (...) with a quantificational apparatus that is “substitutional” rather than “objectual”, and by obtaining from the language so enriched another language in which constants for such predicates apply to singular terms that stand for propositions. (shrink)

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

Recently, there’s been a lot of interest in a research program that tries to understand propositional representation in terms of the subject’s performance of sub-propositional mental acts like reference and predication (e. g. Burge 2010, Hanks 2015, Soames 2010, 2015). For example, on one version of the view, for a subject to predicate the property of being a composer of Arvo just is what it is to perform the to the basic propositional act of judging that Arvo is a (...) composer (e. g. Hanks 2015). In this paper I first present my own version of this view and contrast it with alternatives. I then argue that we must clearly separate the thin predication-resultant notion of judging (S(emantic)-judgment) from a much richer notion used in epistemology (E(pistemic)-judgment). The former is just the act of thinking a forceful thought. The latter is the act of making up one’s mind about how things are, a way of concluding theoretical or doxastic deliberation. I argue that these two acts differ in three ways: levels of propositional attitude, objective vs. subjective norms, and the possibility of sub-personal occurrence. (shrink)

Many word forms in natural language are polysemous, but only some of them allow for co-predication, that is, they allow for simultaneous predications selecting for two different meanings or senses of a nominal in a sentence. In this paper, we try to explain (i) why some groups of senses allow co-predication and others do not, and (ii) how we interpret co-predicative sentences. The paper focuses on those groups of senses that allow co-predication in an especially robust and stable way. We (...) argue, using these cases, but focusing particularly on the multiply polysemous word ‘school’, that the senses involved in co-predication form especially robust activation packages, which allow hearers and readers to access all the different senses in interpretation. (shrink)

When, for example, we say of something that it ‘is an object’, or ‘is an event’, or ‘is a property’, we are engaging in categorial predication: we are assigning something to a certain ontological category. Ontological categorization is clearly a type of classification, but it differs radically from the types of classification that are involved in the taxonomic practices of empirical sciences, as when a physicist says of a certain particle that it ‘is an electron’, or when a zoologist says (...) of a certain animal that it ‘is a mammal’, or when a meteorologist says of a certain weather‐phenomenon that it ‘is a hurricane’. Classifications of the latter types presuppose that the items being classified have already been assigned to appropriate ontological categories, such as the categories of object, species, or event. What do categorial predications mean? How are their truth‐conditions to be determined, and how can those truth‐conditions be known to be satisfied? Do they have truthmakers? Questions like these are amongst those addressed in the present paper. (shrink)

Simple taste predications come with an acquaintance requirement: they require the speaker to have had a certain kind of first-hand experience with the object of predication. For example, if I tell you that the creme caramel is delicious, you would ordinarily assume that I have actually tasted the creme caramel and am not simply relying on the testimony of others. The present essay argues in favor of a 'lightweight' expressivist account of the acquaintance requirement. This account consists of a recursive (...) semantics and an account of assertion; it is compatible with a number of different accounts of truth and content, including contextualism, relativism, and purer forms of expressivism. The principal argument in favor of this account is that it correctly predicts a wide range of data concerning how the acquaintance requirement interacts with Boolean connectives, generalized quantifiers, epistemic modals, and attitude verbs. (shrink)

In contemporary philosophy of religion, the two most standard approaches to predicates of God are analogy and univocation. While analogy lacks precision and is best used in liturgical and sacred texts, univocal predicates are problematic because they seem to lead to ontological monism of sameness between God and creatures, which cannot be allowed within metaphysics of Absolute Being. In this article, I examine and contrast G. Frege’s approach to univocal predications and L. Wittgenstein’s notion of language-games, which allows us to (...) move away from univocation as a case of strong identity toward univocation as the extra-linguistic context of human activities. Indeed, that human context can be shared with ‘Goodness,’ ‘Wisdom,’ ‘Simplicity,’ ‘Love’ and many other predicates we attribute to God. I argue that our language of univocal predicates must reflect not the abstract concepts but that same context of divine and human activities in which names of God achieve univocal context. Key words: analogy, univocal predicates, G. Frege, L. Wittgenstein, contextual principle, language-games . (shrink)

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

We argue that a cognitive semantics has to take into account the possibly partial information that a cognitive agent has of the world. After discussing Gärdenfors's view of objects in conceptual spaces, we offer a number of viable treatments of partiality of information and we formalize them by means of alternative predicative logics. Our analysis shows that understanding the nature of simple predicative sentences is crucial for a cognitive semantics.

This paper contrasts the scholastic realisms of David Armstrong and Charles Peirce. It is argued that the so-called 'problem of universals' is not a problem in pure ontology (concerning whether universals exist) as Armstrong construes it. Rather, it pertains to which predicates should be applied where, issues which Armstrong sets aside under the label of 'semantics', and which from a Peircean perspective encompass even fundamentals of scientific methodology. It is argued that Peirce's scholastic realism not only presents a more nuanced (...) ontology (distinguishing existence and reality) but also illuminates why scholastic realism is a position worth fighting for. (shrink)

In this paper I revisit the main arguments for a predicate analysis of descriptions in order to determine whether they do in fact undermine Russell's theory. I argue that while the arguments without doubt provide powerful evidence against Russell's original theory, it is far from clear that they tell against a quantificational account of descriptions.

This is a defence of the claim that names are predicates with a demonstrative element in their singular use.

Reconstructs the original Greek version of the confatalia-argument that Cicero attributes to Chrysippus in De fato and misrepresent in crucial ways. Compares this argument with Seneca's discussion of determinism in the Naturales quaestiones. Clarifies that Seneca makes a different distinction from that attested in Cicero's De fato. Argues that problems with interpreting both accounts derive from disregarding terminological distinctions harder to spot in the Latin versions and, related to this, insufficient attention to the ontological distinction between bodies (such as Fate) (...) and predicates (e.g. "what is fated"), which unfortunately does not square well with the modern ontological category "event." Contains some corrections to the author's earlier discussion of the topic in Seneca und die Stoa: Der Platz des Menschen in der Welt, De Gruyter 2006, ch. 3.3.4. (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 argue there are two ways predication relations can hold according to the Categories: they can hold directly or they can hold mediately. The distinction between direct and mediated predication is a distinction between whether or not a given prediction fact holds in virtue of another predication fact’s holding. We can tell Aristotle endorses this distinction from multiple places in the text where he licenses an inference from one predication fact’s holding to another predication fact’s holding. The best explanation for (...) each such inference is that he takes some predication facts to be mediated by others. Once the distinction between direct and mediated predication has been explained and argued for, I show how it can help solve a persistent problem for the traditional view of non-substantial particulars in the Categories—that is, the view that non-substantial particulars are particular in the sense of being non-recurrent. Along with vindicating the traditional view, the direct/mediated predication distinction gives us a distinctive way of understanding what it is for something to be recurrent (or non-recurrent) as well as a better understanding of Aristotle’s broader commitments in the Categories as a whole. (shrink)

Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality in mathematics. The notion of an adjunction (a pair of adjoint functors) has moved to center-stage as the principal lens. The central feature of an adjunction is what might be called “determination through universals” based on universal mapping properties. A recently developed “heteromorphic” theory (...) about adjoints suggests a conceptual structure, albeit abstract and atemporal, for how new relatively autonomous behavior can emerge within a system obeying certain laws. The focus here is on applications in the life sciences (e.g., selectionist mechanisms) and human sciences (e.g., the generative grammar view of language). (shrink)

There are many examples offered as evidence that proper names are predicates. Not all of these cases speak to a name’s semantic content, but many of them do. Some of these include attributive, quantifier, and ambiguity cases. We will explore those cases here, and we will see that none of them conclusively show that names are predicates. In fact, all of these constructions can be given alternative analyses that eliminate the predicative characteristics of names they feature. These analyses do not (...) involve having names functioning as predicates in any way at all. In attributive cases, the names within them are to be understood as occurring in a comparative construction, not an attributive construction. In the last two sorts of cases, the names that occur are analyzed as part of a more complex referring device for a specific domain, rather than functioning as predicates. Both paraphrases can be given plausible semantic treatments that have significant advantages over their competitors. For this reason, there is less motivation to focus on predicative views of proper names. (shrink)

Along with many other languages, English has a relatively straightforward grammatical distinction between mass-occurrences of nouns and their countoccurrences. As the mass-count distinction, in my view, is best drawn between occurrences of expressions, rather than expressions themselves, it becomes important that there be some rule-governed way of classifying a given noun-occurrence into mass or count. The project of classifying noun-occurrences is the topic of Section II of this paper. Section III, the remainder of the paper, concerns the semantic differences between (...) nouns in their mass-occurrences and those in their count-occurrences. As both the name view and the mixed view are, in my opinion, subject to serious difficulties discussed in Section III.1,I defend a version of the predicate view. Traditionally, nouns in their singular count-occurrences are also analyzed as playing the semantic role of a predicate. How, then, does the predicate view preserve the intuitive difference between nouns in their mass- and those in their count-occurrences? I suggest, in Section III.2, that there are different kinds of predicates: mass-predicates, e.g. ‘is hair’, singular count-predicates, e.g. ‘is a hair’, and plural count-predicates, e.g. ‘are hairs’. Mass-predicates and count-predicates, in my view, are not reducible to each other. The remainder of Section III takes a closer look at the differences and interrelations between these different kinds of predicates. Mass-predicates and count-predicates differ from each other truth-conditionally, and these truth-conditional differences turn out to have interesting implications, in particular concerning the part-whole relation and our practices of counting. But mass- and count-predicates are also related to each other through systematic entailment relations; these entailment relations are examined in Section III.4. (shrink)

Predication is a lingual relation. We have this relation when a term is said (λέγεται) of another term. This simple definition, however, is not Aristotle’s own definition. In fact, he does not define predication but attaches his almost in a new field used word κατηγορεῖσθαι to λέγεται. In a predication, something is said of another thing, or, more simply, we have ‘something of something’ (ἓν καθ᾿ ἑνὸς). (PsA. , A, 22, 83b17-18) Therefore, a relation in which two terms are posited (...) to each other in a way that one is said (predicated) of the other is a predication. The term of which the other term is said is called a subject (ὑποκειμένον) and the other, which is said about the subject, is called the predicate. Thus, in a predication the predicate is predicated of the subject; given that being predicated is almost as the same as being said. The relation between being said and being predicated is so close that ‘if something is said of a subject both its name and its definition are necessarily predicated of the subject.’ (Cat., 5, 2a19-26) This, however, is true only about the second genera and not the accidents. a) Nature of relation in predication What is Aristotle’s theory about the nature of the relation in a predication? How does he fundamentally understand this relation? Phil Corkum distinguishes between predication logic and traditional term logic and argues that the relation between subject and predicate in Aristotle is of the latter kind. While in predicate logic, subjects and predicates have distinct roles, they have the same role in traditional term logic. In predication logic, subjects refer, but predicates characterize. Thereupon, a sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. In traditional term logic, both subjects and predicates refer and a sentences expresses a truth if both name one and the same thing. He concludes that Aristotle ‘problematically conflates prediction and identity claims’ because while he thinks both subjects and predicates refer, he would deny that a sentence is true just in case the subject and the predicate name one and the same thing. Based on this, Corkum believes that Aristotle’s core semantic is not identity but the weaker relation of constitution, which is a mereological interpretation: ‘All men are mortal’ is true just in case the mereological sum of humans is part of the mereological sum of mortals. b) Aristotle’s theory of predication: one or two theories? Frank Lewis finds an inconsistent gap between the theory of predication in the Categories and that in the later books of the Metaphysics VII, 6. So too Joan Kung, Terry Irwin, Daniel Graham. c) Distinction of ‘being said of’ and ‘being in’ Owen enumerates the texts in which Aristotle’s distinction between ‘being said of’ and ‘being in’ is asserted: OI. 11b38-12a17; To., 127b1-4; Cat. 1a20-b9; 2a11-14; 2a27-b6; 2b15-17; 3a7-32; 9b22-24 d) Predication in Aristotle and the standard ‘S is P’ Marie De Rijk Lambertus thinks that the ‘S is P’ pattern is misleading when it comes to express predication in Aristotle. In his view, ‘The Aristotelian procedure should be described in terms of appositively assigning an attribute (κατηγορούμενον) to a substrate (ὑποκείμενον), rather than ascribing a predicate to a subject by means of a copula…. The comment should be considered an attribute which is said to fall to a substrate, without understanding this procedure in terms of sentence predication.’ e) Aristotle’s predication: bipartite or tripartite? It is a difficulty to make Aristotle’s theories of name-verb predication and tripartite predication consistent. The reason is that tripartite is not consistant with his name-verb structure based on which he says that the predicate term is the ‘verb.’ (20a31; 20b1-2; 16a13-5) The problem is that in a tripartite form like ‘Socrates is white’ we cannot take ‘is white’ as the verb because, based on Aristotle himself, no part of a verb can be significant itself. (16b6-7) However, his assertions about the equivalences between the two structures (OI. 12, 21b9-10; PrA. 51b13-16; Met., 1017b22-30) must mean that they are not inconsistent in his own view. Thus, as Allen Bāck points, ‘Aristotle seems to think that he has a single, consistent theory.’ The sense of saying or speaking as the root sense of rhema makes the relation between predication (saying something of something) and verb more interesting. The use of rhema in the sense of a long expression approves this. In Plato’s work (399ac) where Socrates claims that the name anthropos derives from anthron ha opopen (‘he who examines what he has seen’) we have an onoma from, or in place of, a rhema. 1) Subject The subject (ὑποκειμένον) is that of which another term is said or predicated. Aristotle’s own definition is of a much more philosophical value: ‘By subject I mean that which is expressed by an affirmative term (λέγω δὲ ὑποκείμενον τὸ κάταφάσει δηλούμενον).’ (Met., K, 1067b18) Throughout Aristotle’s work, three kinds of subjects can be found: possible, prime and absolute subject. a) Possible subject Those things that can take the position of a subject in a predication we call possible subjects, no matter they can or cannot take the position of predicate in any predication. All terms except the ultimate predicates are possible subjects because they can take the position of subject. b) Prime subject Those that in any predication can only take the position of a subject and not the position of a predicate are prime subjects. (Cat., 5, 3a36-b2; Met., Z, 1028b36-1029a1) This is the truest sense of subject and belongs only to substances. (Met., Z, 1029a1-2) In fact, ‘that which is not predicated of a subject, but of which all else is predicated’ is a substance. (Met., Z, 1029a7-9) In Categories, besides primary substances (Cat., 2, 1b3-6), individual qualities are also said not to be able to be said of anything else. (Cat., 2, 1a23-29) Aristotle’s examples are a certain ‘knowledge-of-grammar’ (τὶς γράμματικὴ) and ‘an individual white’ (τὸ τὶ λευκὸν). Thus, although substances are indeed in the truest sense individuals and, thereby, in the truest sense primary subjects, other individuals can take the position of subject as well. c) Absolute subject While substances are prime subjects of all other things, there is still something of which substances can be predicated and this predication is not an accidental predication: matter. (Met., Z, 1029a21-24) This predication is, indeed, the predication of a ‘form or this’ on matter and material substance. (Met., Θ, 1049a34-36) The only thing that is absolutely a subject, therefore, and can be a predicate is prime matter (πρώτη ὓλη). (Met., Θ, 1049a24-27) d) Subject and substance The most important thing in being a substance is being a subject: ‘It is because the primary substances are subjects for all the other things and all the other things are predicated of them or are in them, that they are called substances most of all.’ (Cat., 5, 2b15-17) And what is nearer to this position is more a substance as a species is more a substance than a genus.’ (Cat., 5, 2b7-8) e) Primary versus accidental subject A subject is a primary subject in a predication when the predicate is predicated of it as itself. In such a case, the subject is the subject of the predicate qua itself and not qua something else. A subject, on the one hand, is an accidental subject when it is not the primary subject of the predicate that is predicated on it. It means that a subject is an accidental subject when the predicate is predicated of it not qua itself but qua something else. An accidental subject is, therefore, anything other than a substance. 2) Predicate as universal It is evident from our discussion of kinds of subjects that except matter, primary substances (if we ignore both accidental predication and cases of absolute subjects) and other individuals, everything else can take the position of a predicate. Since primary substances are individuals, it results that everything except matter and individuals are capable to take the position of predicate. The immediate consequence of this is that the predicate must be a universal. When individuals cannot take the position of predicate, this position cannot be taken by any particular. Therefore, only universals can be predicated of others. Moreover, albeit universals can be a simple subject (for another universal), they are not prime subjects. The closeness of universal and predicate is to the extent that Aristotle differentiates universal from subject. (Met., Θ, 1049a27-30) 3) Categories or classes of predicates Aristotle distinguishes ten highest classes into one of which each predicate must necessarily fall: substance (or what a thing is), quality, quantity, relation, place, time, position, state, activity and passivity. (Cat., 4, 1b25-27; To., I, 9, 103b20- ; PsA., A, 22, 83b13-23) The substance counted among predicates must refer to secondary and not primary substances not only because Aristotle insists that primary substances cannot be predicated but also from his own examples of the category of substance: man and animal. (To., I, 9, 103b25) However, if a predicate be asserted of itself or its genus be asserted of it, the predicate signifies substance or what is; but if ‘one kind of predicate is asserted of another kind,’ it signifies one of the other nines. (To., I, 9, 103b30) These categories are so comprehensive that no predicate can remain outside them so that even non-being has as many senses as categories. (Met., M, 1089a26-30) a) That whether Aristotle’s categories are merely linguistic or fundamentally ontological is a so much controversial dispute. Some like G. E. R. Lloyd believe that ‘categories are primarily intended as a classification of reality … rather than of the signifying terms themselves.’ b) Although Aristotle’s categories have been historically regarded as a classification of predications, there are some recent commentators like Jonathan Barnes that think it is classifying predicates and not predications. 4) Kinds of predicates In his introduction of Categories, as J. W. Thorp truly points out , Aristotle distinguishes between the category of substance and the other categories using μὲν ... δὲ construction. This construction illustrates that beside tenfold classification of categories, there is an even more crucial differentiation between two kinds of predicates: substance or what is on the one hand and the other nine ones on the other hand: the distinction between what is predicated of the subject as what it is and what is predicated of it as an accident. Therefore, we have three kinds of classification - a twofold, a fourfold and a tenfold-complicatedly classifying the same thing, viz. the predicate. Predicates can be divided also to four kinds: property, definition, genus and accident. (To., I, 4, 101b11-20) A property is that predicate that is convertible with its subject and does not signify its essence. A definition is that predicate that is convertible with its subject and signifies its essence. It is a genus if it is not predicated convertibly and is contained in the definition of its subject. And it is an accident if it is neither convertible nor contained in the definition of its subject. (To., I, 8, ^103b3) All of these four kinds are among categories. (To., I, 9, 103b20) It seems that there might be some kind of relation between the twofold and the fourfold distinction: whereas genus and definition are predicated as what it is, accidents are not so predicated. There seems to be some rules that determine to each of these four kinds each predicate belongs. At To., IV, 123b30ff. Aristotle asserts: ‘If B has a contrary and A does not, then B does not belong to A as its genus.’ There is a dispute around per se accidents (τὰ καθ’ αὑτὰ συμβεβηκότα) (Topics., 102a18) whether they must be regarded as either of the four kinds or as a fifth kind. Barnes (1970) argued that they ‘do not fit at all neatly into the fourfold classification.’ He argues that based on the definition of accidents at A, 5, 102b4-5, they must be accidents but based on another definition, A, 5, 102b6-7, they cannot be accidents. He also defends the view that they are not properties. Barnes concludes: ‘This shows that the two definitions are not equivalent, and hence that the ‘predicables’ are not well-defined.’ Demetris J. Hadgopoulos defends the view that the two definitions of accidents are equivalent and per se accidents are properties. 5) Five types of predications We have five kinds of predications based on our division of subjects and our discussion of predicates: simple, primary (itself divided to substantial and accident), accidental (itself divided to primary and secondary), aoincidental and absolute predication. a) Simple predication. This is a predication in which a universal is predicated of either a particular or a universal subject. This sense of predication includes all other senses except the first kind of accidental predication. b) Primary predication. This is a predication in which a universal is predicated of a primary subject, namely a substance. A primary predication is of two kinds: i) Substantial predication. A primary predication in which the predicate is part of, or is included in, the definition of the subject. The universal that is the predicate here is the definition or the genus or the species or the diferentia of the subject. It is this predication that Aristotle calls a unity: ‘A statement may be called a unity … because it exhibits a single predicate as inhering not accidentally in a single subject.’ (PsA., B, 10, 93b35-37) It is only substantial predicates that can be predicated of each other: ‘Predicates which are not substantial are not predicated of one another.’ (PsA., A, 22, 83b18-19) Aristotle defines a substantial predication also in another way. A predication in which a higher genus is predicated on a lower genus, species, a substance or an individual, (or a species is predicated on an individual) is a substantial predication. Therefore, a substantial predication is a predication in a series that has individuals on one of its ends and a general category on its other end. In fact, only substantial predicates can be predicated of one another. (PsA., A, 22, 83b17-19) This series cannot be an infinite series because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) -/- ii) Accident predication. A primary predication in which the predicate is not part of, or is not included in, the definition of its subject. The universal that is the predicate here is the property or the accident of the subject. c) Accidental predication. This is a predication in which the subject is not a primary subject and its predicate is a substance. This predication is of two kinds: i) Primary accidental predication. This is a predication in which an accident is predicated of substance. Such a predication can go ad infinitum, which is inferable from Aristotle’s assertion that the secondary accidental predication cannot go ad infinitum. ii) Secondary accidental predication. It is a predication in which an accident is predicated of another accident. Such a predication, Aristotle asserts, cannot go ad infinitum because even more than two accidents cannot be combined. Now what is the meaning of Aristotle’s assertion that we cannot continue this ad infinitum? Does it mean that we cannot continue the predication ‘The musician is white’ and say ‘The white is Athenian?’ But why not? Or maybe he means that by adding any predication, we are still in a condition of predicating two accidents of a substance on each other. -/- As primary subjects, substances can also take the position of predicate though not essentially but accidentally. In propositions like ‘the white is a log’ or ‘That big thing is a log’ we observe substance taking the position of predicate but this is only accidentally: ‘When I affirm ‘the white is a log,’ I mean that something which happens to be white is a log- not that white is the subject in which log inheres (οὐχ ὡς τὸ ὑποκείμενον τῷ ξύλῳ τὸ λευκόν ἐστι), for it was not qua white or qua a species of white that the white (thing) came to be a log (οὔτε λευκὸν ὄν οὔθ᾿ ὃπερ λευκόν τι ἐγἐνετο ξύλον), and the white (thing) is consequently not a log except incidentally.’ (PsA., 22, 83a3-9) Aristotle compares this accidental use of substance in the position of predicate with the substantial use of it in the place of a subject: ‘On the other hand, when I affirm ‘the log is white,’ I do not mean that something else, which happens to be a log, is white (οὐχ ὃτι ἓτερόν τί ἐστι λευκόν, ἐκείνῳ δὲ συμβέβηκε ξύλῳ εἶναι), (as I should if I said ‘the musician is white,’ which would mean ‘The man who happens also to be a musician is white’); on the contrary, log is here the subject- the subject which actually came to be white, and did so qua wood or qua a species of wood and qua nothing else.’ (PsA., 22, 83a8-14) Aristotle asks us not to call propositions like ‘The white is a log’ a predication at all or at least call them accidental predication instead of simple (ἁπλως) predication. (PsA., A, 22, 83a14-17) An accidental predication, in which we have a substance in the place of predicate, is different from an essential predication in that while the subject of an accidental predication is said to be the predicate not by itself but as something different with which it coincides, the subject of an essential predicate is said to be the predicate by itself and not because it is something else: ‘Since there are attributes which are predicated of a subject essentially and not accidentally- not, that is, in the sense in which we say ‘That white (thing) is a man,’ which is not the same mode of predication as when we say ‘The man is white’: the man is white not because he is something else but because he is man, but the white is man because ‘being white’ coincides with ‘humanity’ within one subject. Therefore, there are terms such as are essentially subjects of predicates. (PsA., A, 19, 81a24-29) This capability of ‘non-essentially and only accidentally’ being a subject does belong, in fact, to all sensible things. (PsA., A, 27a32-36) d) Coincidental predication. this is a predication in which none of the subject and predicate are a substance or an individual. In this predication, one of the accidents of a substance or individual is predicated of one of the other accidentals of the same substance or individual. For example, when it is said that ‘The white is musical,’ there is an individual, say Socrates, for which both of white and musical are accidents. e) Absolute predication. This is a predication in which a form or a substance is predicated of a matter or a material substance. Some commentators like Loux and Lewis regarded this predication as close to accident predication, both based on inherence. As R.M. Dancy points out, these predications make Aristotle’s theory of predication immanentist: not only accident predications are explained by the immanence of accidents in substances, some of the substantial predications, which were not explained in Categories, are also explained by the immanence of form in matter. It is interesting that in this kind of predication, it is the predicate and not the subject, which is in the strictest sense substance. As the central books of Metaphysics claim, the form is the substance. Thus, in this predication, substance gets away from the sense of ὑποκείμενον. Corkum mentiones 68a19 as the only instance where Aristotle explicitly claims that a term may be predicated of itself, a passage that is, in Corkum’s view, problematic. 6) Demonstrable predicates Those predicates are demonstrable that are so related to their subjects that there are other predicates prior to them predicable of their subjects (ἔτι δ᾿ ἄλλος, εἰ ὧν πρότερα ἄττα κατηγορεῖται). (PsA., A, 22, 83b32-34) 7) Series of predications Since it is possible for a predicate to be itself the subject of another predication, we can have a series of predications in which the predicate of a predication is the subject of the next predication. This series has the following features: a) It has a limit (in number) (PsA., A, 22, 83b14-16) on the side of subjects: there are subjects that cannot themselves be predicated (PsA., A, 27, 43a39-41), which are, as we noted, prime subjects: particulars, i.e. prime substances and other individuals. (PsA., A, 19-22) Aristotle calls them ultimate (ὓστατον). (PsA., 21, 82a36-b1) b) It has a limit (in number of kinds) (PsA., A, 22, 83b14-16) also on the side of predicates: there must be predicates that cannot be subjects. (PsA., A, 19-22; PsA., A, 27, 43a36-39) Aristotle calls them primary (πρῶτον). (PsA., A, 21, 82b1-4) These are the highest categories or the highest genera of categories. (PsA., A, 22, 83b14-16) c) The series has an escalating shape from mere subjects at its downside to mere predicates at its upside. It is Aristotle himself whos uses the words up and down in this sense. (e.g. PsA., A, 22, 83b2-3) d) The predications that lie between lowest and highest ones must be finite in number. (PsA., A, 19-22 especially: 20, 82a21-35) These have subjects and predicates, each capable of both of the roles of being subject and being predicated. A result of this fitness is that neither demonstration can go to infinity nor everything is demonstrable, the two points Aristotle always insist on. e) The upward side includes the more universal ones and the downward the more particular ones. (PsA., 20, 82a21-23) f) It follows from the above features that ‘neither the ascending nor the descending series of predications … are infinite.’ (PsA., A, 22, 83b24-25) g) Reciprocation and convertibility. Except in case of terms (i.e. subjects and predicates) that are at each of the ends of series of predications, namely ultimates and primaries, it is possible to reciprocate (ἀντιστρέφειν) terms and convert the predication. (PsA., A, 19, 82a15-20) h) Antipredication. Antipredication means that in a predication (S is P), the subject becomes the predicate of its predicate (P is S) in the same category its predicate was predicated on it. For example, if P is in the category of quality, antipredication means that S be predicated of P in the category of quality. In other words, P is a quality of S and S is a quality of P. Aristotle rejects this. (PsA., A, 22, 83a36-b3) i) Self-predication versus other-predication. Aristotle distinguishes between a predication in which a term is said of itself and a predication in which a term is said of another. (Phy., Δ, 2, 209a31-33) j) Predicablity (Cat., 5, 3a36-b2): 1) Primary substances and individuals are not predicable. 2) Secondary substances are of two kinds: genus and species i) Genus is predicable able both of the species and of the individuals. ii) Species is predicable of the individual. 3) Differentiae are predicable both of the species and of the individuals. 8) Predication as classification a) Richard Patterson believes that Aristotle’s so repeated construction using hoper (estin A hoper B) in Topics (120a23 sq., 122b19, 26sq., 123a, 124a18, 125a29, 126a21, 128a35. Also in Posterior Analytics (83a24-30) (Brunschwig’s list. ‘expresses the fact that A is a kind of B (esti A B tis), that A is a species of the genus B.’ 9) Universal predication Aristotle defines universal predication (κατὰ παντὸς κατηγορεῖσθαι) as such: ‘wherever no instance of the subject (τῶν τοῦ ὑποκειμέμνου) can be found of which the other term cannot be asserted.’ (PrA., A, 24b27-29) In this predication, the subject is included in another as in a whole (ἐν ὃλῳ εἶναι) and the predicate is predicated of all of the subject (κατὰ παντὸς κατηγορεῖσθαι). (PrA., A, 24b26-27) Attach another discussion we had about ἐν ὃλῳ here. 10) Quantity of predication A predication, truly stated, has a quantity, which is the number of objects under the name of the subject of which the predicate is predicated. The quantity of subject can be stated in four ways: a. Indefinite: when the predicate belongs or does not belong to the subject without any mark to show to haw many of the particulars under the name of the subject it does or does not belong. E.g. ‘Man is white’; ‘Man is not white.’ (PrA., A, 24a20; OI., I, 7, 17b8-12) b. Universal quantity: When the predicate belongs to all or none of the subject. E.g. ‘Every man is animal’; ‘No man is animal.’ (PrA., A, 24a18-19; OI., I, 7, 17b5-6) The contrary of a predication of a universal quality is a predication of a universal quality. E.g. the contrary of ‘Every man is white’ is ‘No man is white.’ (OI., I, 7, 17b20-23) c. Particular quantity: When the predicate belongs (or does not belong) to some of the subject. E.g. ‘Some men are white’; ‘Some men are not white.’ (PrA., A, 24a19-20) d. Single quantity: when the subject is a proper name of only one object. E.g. ‘Socrates is white’; ‘Socrates is not white.’ The contrary of this predication is of a single quantity: ‘Socrates is not white.’ (OI., I, 7, 17b38-18a4) 11) Convertibility of predication. Some predications are convertible, that is, it is possible to change the place of subject and predicate in a true proposition so that the converted proposition remains true. This is supposed to mean that given the truth of a predication, the truth of the converted predication is inferable. The convert form of a predication depends on its quantity. a. Indefinite quantity: This predication has no strictly true convert because its quantity is not stated. b. Universal quantity: It can be converted in two ways: i) A negative universal can be converted to a negative universal in which the terms are changed. E.g. ‘No pleasure is good’ can be converted to ‘No good is pleasure.’ (PrA., A, 2, 25a5-8 and a14-19) ii) An affirmative universal can be converted to an affirmative particular in which the terms are changed. E.g. ‘Every pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a7-9) c. Particular quantity: If it is negative, it cannot be converted but if it is affirmative, it can be converted to an affirmative predication with particular quantity. E.g. ‘Some pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a10-13 and a20-24) d. Single quantity: It cannot be converted. 12) Characteristics of relations between subject and predicate 1. A predicate is of a wider range than its subject. It is based on this fact that Aristotle: a) Prevents individuals to be predicate because there is nothing of which an individual be of a wider range. In other words, it is due to the fact that since an individual is only ‘one particular’ thing and, thus, cannot be of a wider extent than anything that Aristotle prevents them of being a predicate. Matthews, however, thinks we cannot use Socrates, a substance and an individual, in the place of predicate and say it of Socrates because ‘Socrates does not classify Socrates: it names him.’ b) Prevents differentia, species and things under species to be predicated of genus. (To., Z, 6, 144a27-) c) Prevents the species and the things under it to be predicated of the differentia. (To., Z, 6, 144b1-4) d) Also about the effect because it is wider than its subject. (PsA., B, 17, 99a) e) Each attribute is wider than every individual it is predicated on, though several attributes, collectively considered, might not be wider but exactly the substance of a thing. (PsA., B, 13, 96a32-b1) 2. The predicate of a predicate of a subject will be predicated of the subject too: ‘whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject too.’ (Cat., 3, 1b10-15) In fact, it is due to its predication of the subject that it is predicated of its predicate. (Cat., 5, 2a36-b1) Moreover, what is not predicated of the predicate of a subject cannot be predicated of it as well. (PrA., A, 27, 43b22-27) Thus, what, for example, is not predicated of animal, cannot be predicated of man. 3. The predicate of a subject can be predicated of its predicates as well. (Cat., 5, 3a1-6) For example, you call the individual man grammatical and, thence, you call both a man and an animal grammatical. Nonetheless, the predicate of a subject belongs to it more properly than to its higher predicates. (PrA., A, 27, 43a27-32) 4. It is only the subject that can be distributed and not the predicate. (PrA., A, 27, 43b16-22; OI, I, 7, 17b12-16) Therefore, we can say e.g. ‘Every man is animal’ but we cannot say ‘Every man is every animal.’ 5. It is the reason of the relation between subjects and predicates, that is the reason of predication, which is the subject of inquiry. (Met., Z, 1041a20-24) In other words, since it is a meaningless inquiry to ask why a thing is itself (Met., Z, 1041a14-15), the only remaining meaningful inquiry is to ask why something is something else, i.e. to ask about the reason of predication. 6. A subject cannot categorize its predicate in the same category in which it is categorized by it. If e.g. A is a quality of B, B cannot be a quality of A. Therefore, there is no reciprocation in the same category. (PsA., A, 22, 83a36-39) 13) Characteristics of series of predications 1. A series of secondary accidental predication cannot go ad infinitum for not even more than two terms can be comnbined. For an accident is not an accident of an accident, unless it be because both are accidents of the same subject. (Met., Γ, 1007b1-4) 2. Infinite series cannot be traversed in thought. (PsA., A, 22, 83b6-7) 3. The predications of genera on each other must be ended and cannot go to infinity because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) Therefore, a series of predication of genera on each other must be limited on both sides. There must be an upward limit in general categories as well as a downward limit in individual because they cannot be predicated of others. Whatever lies between these limits can both be predicated of others and others be predicated of them. (PrA., A, 27, 43a36-43) 4. The order of predicates matters: it makes a difference whether the series be ABC or BAC. (PsA., B, 13, 96b25-32) . (shrink)

In this paper, I respond to criticisms of my book Being and Reason recently made by Yitzhak Melamed.

I here respond to Pietro Salis’s objections against my original critique of the Prosentential Theory of Truth. In addition, I clarify some points regarding the relationship between anaphoric relationships and “general semantic notions” like “equivalence”, “consequence”, and “sameness of content”, and make some further points about ’s ability gto explain pragmatic and expressive features of “true”.

In the debate between relativism and contextualism about various expressions, the Operator Argument, initially proposed by Kaplan , has been taken to support relativism. However, one widespread reaction against the argument has taken the form of arguing against one assumption made by Kaplan: namely, that certain natural language expressions are best treated as sentential operators. Focusing on the only extant version of the Operator Argument proposed in connection to predicates of personal taste such as “tasty” and experiencer phrases such as (...) “for Anna” ), in this paper I investigate whetherthe reasons offered by Cappelen and Hawthorne against various assumptions of the argument failing in the case of modal, temporal, locationaland precisional expressions transfer to the case of experiencer phrases to undercut support for relativism about predicates of personal taste. My aim is to show that they don’t. Thus, I first show that their considerations against experiencer phrases such as “for Anna” being sentential operators are not decisive. Second, I show that even if granting that such experiencer phrases are not sentential operators, a suitably modified version of the Operator Argument can be defended from the objections they raise. (shrink)

Many accept David Lewis's (1983) claim that, among the candidate meanings for our predicates, some are more natural than others -- they do better or worse at ``carving nature at its joints''. Call this claim predicate naturalism. Disagreement remains over whether the notion of naturalness extends ``beyond the predicate'' (à la Sider, 2011). Are the candidate meanings of logical vocabulary also more or less natural? Call this claim logical naturalism. -/- One motivation for predicate naturalism comes from (...) its supposed ability to help rebut various radical indeterminacy arguments associated with Hilary Putnam (1977, 1980, 1981). It does so in combination with a popular meta-semantic theory called reference magnetism. I argue that the same threats of Putnam-style radical indeterminacy rearise for proponents of predicate naturalism -- threats which logical naturalism helps rebuts. So, if we accept predicate naturalism because it helps fend off threats of indeterminacy, we should also accept logical naturalism. (shrink)

Moral particularism, on some interpretations, is committed to a shapeless thesis: the moral is shapeless with respect to the natural. (Call this version of moral particularism ‘shapeless moral particularism’). In more detail, the shapeless thesis is that the actions a moral concept or predicate can be correctly applied to have no natural commonality (or shape) amongst them. Jackson et al. (Ethical particularism and patterns, Oxford University Press, Oxford, 2000) argue, however, that the shapeless thesis violates the platitude ‘predication supervenes (...) on nature’—predicates or concepts apply because of how things are, and therefore ought to be rejected. I defend shapeless moral particularism by arguing that Jackson et al’s contention is less compelling than it firstly appears. My defense is limited in the sense that it does not prove shapeless moral particularism to be right and it leaves open the possibility that shapeless moral particularism might attract criticisms different from the ones advanced by Jackson et al. But at the very least, I hope to say enough to undermine Jackson et al’s powerful attack against it. The plan of this paper is as follows. Section 1 glosses the view of moral particularism and why it is taken to be essentially committed to the shapeless thesis. Section 2 examines a Wittgensteinian argument for the shapeless thesis. I shall argue that the Canberrans’ counter-arguments against it on grounds of disjunctive commonality and conceptual competence do not succeed. Section 3 explicates Canberrans’ predication supervenience argument against the shapeless thesis. Section 4 offers my criticisms of the Canberrans’ predication supervenience argument. In view of the above discussions, in Sect. 5, I conclude that there is no compelling argument (from the Canberrans) to believe that the shapeless thesis fails (as I have argued in Sect. 4). In fact, there is some good reason for us to believe it (as I have argued in Sect. 2). If so, I contend that moral particularism, when construed as essentially committed to the shapeless thesis, still remains as a live option. (shrink)

This work gives an extended presentation of the treatment of variable-binding operators adumbrated in [3:1993d]. Illustrative examples include elementary languages with quantifiers and lambda-equipped categorial languages. Some remarks are also offered to illustrate the philosophical import of the resulting picture. Particularly, a certain conception of logic emerges from the account: the view that logics are true theories in the model-theoretic sense, i.e. the result of selecting a certain class of models as the only “admissible” interpretation structures (for a given language).

First, given criteria for identifying universals and particulars, it is shown that stuffs appear to qualify as neither. Second, the standard solutions to the logico-linguistic problem of mass terms are examined and evidence is presented in favor of the view that mass terms are straightforward singular terms and, relatedly, that stuffs indeed belong to a metaphysical category distinct from the categories of universal and particular. Finally, a new theory of the copula is offered: 'The cue is cold', 'The cube is (...) ice', and 'Ice is water' all have the form 'A is B'. On the basis of the logical behavior of stuff-names with respect to this univocal copula, definitions are suggested for 'X is a stuff', 'X composes Y', 'X is a material object', and even 'Matter'. Hence an expanded form of logicism. (shrink)