We apply the technique of generic ultrapowers to study the splitting problem of stationary subsets of P K λ . We present some conditions which guarantee the splitting of stationary subsets of P K λ.

It is known that there is a close relation between Prikry forcing and the iteration of ultrapowers: If U is a normal ultrafilter on a measurable cardinal κ and 〈Mn, jm,n | m ≤ n ≤ ω〉 is the iteration of ultrapowers of V by U, then the sequence of critical points 〈j0,n | n ∈ ω〉 is a Prikry generic sequence over Mω. In this paper we generalize this for normal precipitous filters.

If $U$ is a normal ultrafilter on a measurable cardinal $\kappa$, then the intersection of the $\omega$ first iterated ultrapowers of the universe by $U$ is a Prikry generic extension of the $\omega$th iterated ultrapower.

We prove that a Spector‐like ultrapower extension ???? of a countable Solovay model ???? (where all sets of reals are Lebesgue measurable) is equal to the set of all sets constructible from reals in a generic extension ????[a], where a is a random real over ????. The proof involves the Solovay almost everywhere uniformization technique.

If $U_\alpha$ is a length $\omega_1$ sequence of normal ultrafilters on a measurable cardinal $\kappa$ that is increaing w.r.t. the Mitchel order, then the intersection of the $\omega_1$ first iterated ultrapowers of the universe is a Magidor generic extension of the $\omega_1$th iterated ultrapower.

Working in ZF + DC with no additional use of the axiom of choice, we show how to iterate the extended ultrapower construction of Spector . This generalizes the technique of iterated ultrapowers to choiceless set theory. As an application, we prove the following theorem: Assume V = LU[κ] + “κ is λ-supercompact with normal ultrafilter U” + DC. Then for every sufficiently large regular cardinal ρ, there exists a set-generic extension V[G] of the universe in which there (...) exists for some σ a set S ρ for which one can define an elementary embedding j mapping V to LD[S], where D is the filter in V[G] generated by the closed unbounded filter on ρ. Moreover, we have j = ρ, j = σ, j) = S according to LD[S]), and j = D ∩ LD[S] i s a normal ultrafilter in LD[S] on ρ. (shrink)

Let P be a forcing notion and $G\subseteq P$ its generic subset. Suppose that we have in $V[G]$ a $\kappa{-}$ complete ultrafilter1,2W over $\kappa $. Set $U=W\cap V$.

With less than 0# two generic extensions ofL are identified: one in which ${\aleph_1}$ , and the other ${\aleph_2}$ , is almost precipitous. This improves the consistency strength upper bound of almost precipitousness obtained in Gitik M, Magidor M (On partialy wellfounded generic ultrapowers, in Pillars of Computer Science, 2010), and answers some questions raised there. Also, main results of Gitik (On normal precipitous ideals, 2010), are generalized—assumptions on precipitousness are replaced by those on ∞-semi precipitousness. As (...) an application it is shown that if δ is a Woodin cardinal and there is an ${f:\omega_1 \to \omega_1}$ with ${\|f\|=\omega_2}$ , then after ${Col(\aleph_2,\delta)}$ there is a normal precipitous ideal over ${\aleph_1}$ . The existence of a pseudo-precipitous ideal over a successor cardinal is shown to give an inner model with a strong cardinal. (shrink)

We consider a question of T. Jech and K. Prikry that asks if the existence of a precipitous filter implies the existence of a normal precipitous filter. The aim of this paper is to improve a result of Gitik (Israel J Math, 175:191–219, 2010) and to show that measurable cardinals of a higher order rather than just measurable cardinals are necessary in order to have a model with a precipitous filter but without a normal one.

The purpose of this paper is to propose and explore a general framework within which a wide variety of model construction techniques from contemporary set theory can be subsumed. Taking our inspiration from presheaf constructions in category theory and Boolean ultrapowers, we will show that generic extensions, ultrapowers, extenders and generic ultrapowers can be construed as examples of a single model construction technique. In particular, we will show that Łoś's theorem can be construed as a (...) specific case of Cohen's truth lemma, and we isolate the weakest conditions a filter must satisfy in order for the truth lemma to work. (shrink)

A function f from ω1 to the ordinals is called a canonical function for an ordinal α if f represents α in any generic ultrapower induced by forcing with math formula. We introduce here a method for coding sets of ordinals using canonical functions from ω1 to ω1. Combining this approach with arguments from, we show, assuming the Continuum Hypothesis, that for each cardinal κ there is a forcing construction preserving cardinalities and cofinalities forcing that every subset of κ (...) is an element of the inner model math formula. (shrink)

In this paper we will present a simple condition for an ideal to be nowhere precipitous. Through this condition we show nowhere precipitousness of fundamental ideals onPkλ, in particular the non-stationary idealNSkλunder cardinal arithmetic assumptions.In this sectionIdenotes a non-principal ideal on an infinite setA. LetI+=PA/I(ordered by inclusion as a forcing notion) andI∣X= {Y⊂A:Y⋂X∈I}, which is also an ideal onAforX∈I+. We refer the reader to [8, Section 35] for the general theory of generic ultrapowers associated with an ideal. We (...) recallIis said to be precipitous if ⊨I+“Ult(V, Ġ) is well-founded” [9].The central notion of this paper is a strong negation of precipitousness [1]:Definition.Iis nowhere precipitous ifI∣Xis not precipitous for everyX∈ I+i.e., ⊨I+“Ult(V, Ġ) is ill-founded.”It is useful to characterize nowhere precipitousness in terms of infinite games (see [11, Section 27]). Consider the following gameG(I) between two players, Nonempty and Empty [5]. Nonempty and Empty alternately chooseXn∈I+andYn∈I+respectively so thatXn⊃Yn⊃n+1. After ω moves, Empty wins the game if⋂n<ωXn=⋂n<ωYn= Ø.See [5, Theorem 2] for a proof of the following characterization.Proposition.I is nowhere precipitous if and only if Empty has a winning strategy in G(I). (shrink)

A nonstandard universe is constructed from a superstructure in a Boolean-valued model of set theory. This provides a new framework of nonstandard analysis with which methods of forcing are incorporated naturally. Various new principles in this framework are provided together with the following applications: An example of an 1-saturated Boolean ultrapower of the real number field which is not Scott complete is constructed. Infinitesimal analysis based on the generic extension of the hyperreal numbers is provided, and the hull completeness (...) theorem and the Loeb measure construction are extended to objects in the generic extension of the internal universe. The reduction theory of the Boolean-valued complex numbers are developed as a prototype of the applications to the topological reduction theory of Boolean sheaves or operator algebras. (shrink)

A generalization of Příkrý's forcing is analyzed which adjoins to a model of ZFC a set of order type at most ω below each member of a discrete set of measurable cardinals. A characterization of generalized Příkrý generic sequences reminiscent of Mathias' criterion for Příkrý genericity is provided, together with a maximality theorem which states that a generalized Příkrý sequence almost contains every other one lying in the same extension.This forcing can be used to falsify the covering lemma for (...) a higher core model if there is an inner model with infinitely many measurable cardinals – changing neither cardinalities nor cofinalities. Another application is an alternative proof of a theorem of Mitchell stating that if the core model contains a regular limit θ of measurable cardinals, then there is a model in which every set of measurable cardinals of K bounded in θ has an indiscernible sequence but there is no such sequence for the entire set of measurables of K below θ. (shrink)

We prove that in the Cohen extension adding ℵ3 generic reals to a model of containing a simplified (ω1, 2)‐morass, gap‐2 morass‐definable η1‐orderings with cardinality ℵ3 are order‐isomorphic. Hence it is consistent that and that morass‐definable η1‐orderings with cardinality of the continuum are order‐isomorphic. We prove that there are ultrapowers of over ω that are gap‐2 morass‐definable. The constructions use a simplified gap‐2 morass, and commutativity with morass‐maps and morass‐embeddings, to extend a transfinite back‐and‐forth construction of order‐type ω1 (...) to an order‐preserving bijection between objects of cardinality ℵ3. (shrink)

We associate with any abstract logic L a family F(L) consisting, intuitively, of the limit ultrapowers which are complete extensions in the sense of L. For every countably generated [ω, ω]-compact logic L, our main applications are: (i) Elementary classes of L can be characterized in terms of $\equiv_L$ only. (ii) If U and B are countable models of a countable superstable theory without the finite cover property, then $\mathfrak{U} \equiv_L \mathfrak{B}$ . (iii) There exists the "largest" logic M (...) such that complete extensions in the sense of M and L are the same; moreover M is still [ω,ω]-compact and satisfies an interpolation property stronger than unrelativized ▵-closure. (iv) If L = L ωω(Q α ) , then $\operatorname{cf}(\omega_\alpha) > \omega$ and $\lambda^\omega for all $\lambda . We also prove that no proper extension of L ωω generated by monadic quantifiers is compact. This strengthens a theorem of Makowsky and Shelah. We solve a problem of Makowsky concerning L κλ -compact cardinals. We partially solve a problem of Makowsky and Shelah concerning the union of compact logics. (shrink)

We present a novel, perspicuous framework for building iterated ultrapowers. Furthermore, our framework naturally lends itself to the construction of a certain type of order indiscernibles, here dubbed tight indiscernibles, which are shown to provide smooth proofs of several results in general model theory.

The animalist says we are animals. This thesis is commonly understood as the universal generalization that all human persons are human animals. This article proposes an alternative: the thesis is a generic that admits of exceptions. We defend the resulting view, which we call ‘generic animalism’, and show its aptitude for diagnosing the limits of eight case-based objections to animalism.

We generalize the ultrapower in a way suitable for choiceless set theory. Given an ultrafilter, forcing is used to construct an extended ultrapower of the universe, designed so that the fundamental theorem of ultrapowers holds even in the absence of the axiom of choice. If, in addition, we assume DC, then an extended ultrapower of the universe by a countably complete ultrafilter must be well-founded. As an application, we prove the Vopěnka-Hrbáček theorem from ZF + DC only (the proof (...) of Vopěnka and Hrbáček used the full axiom of choice): if there exists a strongly compact cardinal, then the universe is not constructible from a set. The same method shows that, in L[ 2 ω ], there cannot exist a θ-compact cardinal less than θ (where θ is the least cardinal onto which the continuum cannot be mapped); a similar result can be proven for other models of the form L[ A ]. The result for L[ 2 ω ] is of particular interest in connection with the axiom of determinacy. The extended ultrapower construction of this paper is an improved version of the author's earlier pseudo-ultrapower method, making use of forcing rather than the omitting types theorem. (shrink)

In an attempt to address the theoretical gap between linguistics and philosophy, a group of semanticists, calling itself the Generic Group, has worked to develop a common view of genericity. Their research has resulted in this book, which consists of a substantive introduction and eleven original articles on important aspects of the interpretation of generic expressions. The introduction provides a clear overview of the issues and synthesizes the major analytical approaches to them. Taken together, the papers that follow (...) reflect the current state of the art in the semantics of generics, and afford insight into various generic phenomena. (shrink)

Some generic sentences seem to be true despite the fact that almost all the members of the relevant kind are exceptions. It’s controversial whether generics of this type express relatively weak generalizations or relatively strong ones. If the latter, then we’re systematically mistaken about their truth, but they make no trouble for our semantic theorizing. In this brief note, I present several arguments for the former: sentences of the relevant type are weak generics.

A new method is presented for constructing models of set theory, using a technique of forming pseudo-ultrapowers. In the presence of the axiom of choice, the traditional ultrapower construction has proven to be extremely powerful in set theory and model theory; if the axiom of choice is not assumed, the fundamental theorem of ultrapowers may fail, causing the ultrapower to lose almost all of its utility. The pseudo-ultrapower is designed so that the fundamental theorem holds even if choice (...) fails; this is arranged by means of an application of the omitting types theorem. The general theory of pseudo-ultrapowers is developed. Following that, we study supercompactness in the absence of choice, and we analyze pseudo-ultrapowers of models of the axiom of determinateness and various infinite exponent partition relations. Relationships between pseudo-ultrapowers and forcing are also discussed. (shrink)

Consensus has it that generic sentences such as “Dogs bark” and “Birds fly” contain, at the level of logical form, an unpronounced generic operator: Gen. On this view, generics have a tripartite structure similar to overtly quantified sentences such as “Most dogs bark” and “Typically, birds fly”. I argue that Gen doesn’t exist and that generics have a simple bipartite structure on par with ordinary atomic sentences such as “Homer is drinking”. On my view, the subject terms of (...) generics are kind-referring. The interesting truth conditions characteristic of generics arise from the interesting ways in which kinds inherit properties from their members. (shrink)

Against recent work by Haslanger and Leslie, I argue that we do not yet have good reason to think that we should single out generics about social groups out as peculiarly destructive, or that we should strive to eradicate them from our usage. Indeed, I suggest they continue to serve a very valuable purpose and we should not rush to condemn them.

Generics are sentences such as Birds fly, which express generalizations. They are prevalent in speech, and as far as is known, no human language lacks generics. Yet, it is very far from clear what they mean. After all, not all birds fly—penguins don’t! -/- There are two general views about the meaning of generics in the literature, and each view encompasses many specific theories. According to the inductivist view, a generic states that a sufficient number of individuals satisfy a (...) certain property—in the example above, it says that sufficiently many birds fly. This view faces the complicated problem of spelling out exactly how many is “sufficiently many” in a way that correctly captures the intuitive truth conditions of generics. -/- An alternative, the rules and regulations view, despairs from this project and proposes instead that generics directly express rules in the world. Rules are taken to be abstract objects, which are not related to the properties of specific individuals. This view faces the difficult problem of explaining how people come to know of such rules when judging the truth of falsity of generics, and accounting for the strong intuition that a sentence such as Birds fly talks about birds, not abstract objects. -/- What seems to be beyond dispute is that generics, even if they do not express rules, are lawlike: they state non-accidental generalizations. Many scholars have taken this fact to indicate that generics are parametric on possible worlds: they refer to worlds other than the actual world. This, again, raises the problem of how people come to know about what happens in these other worlds. However, a rigorous application of standard tests for intensionality shows that generics are not, in fact, parametric on possible worlds, but only on time. This unusual property may explain much of the mystery surrounding generics. -/- Another mysterious property of generics is that although there is no language without them, there is no linguistic construction that is devoted to the expression of genericity. Rather, generics can be expressed in a variety of ways, each of which can also express nongenerics. Yet, each manifestation of generics differs subtly (or sometimes not so subtly) in its meaning from the others. -/- Even when these and other puzzles of genericity are solved, one mystery would remain: Why are generics, which are so easy to produce and understand in conversation, so difficult to analyze? (shrink)

In the paper we investigate the topos of sheaves on a category of ultrafilters. The category is described with the help of the Rudin-Keisler ordering of ultrafilters. It is shown that the topos is Boolean and two-valued and that the axiom of choice does not hold in it. We prove that the internal logic in the topos does not coincide with that in any of the ultrapowers. We also show that internal set theory, an axiomatic nonstandard set theory, can (...) be modeled in the topos. (shrink)

Generic stereotypes are generically formulated generalizations that express a stereotype, like “Mexican immigrants are rapists” and “Muslims are terrorists.” Stereotypes like these are offensive and should not be asserted by anyone. Yet when someone does assert a sentence like this in a conversation, it is surprisingly difficult to successfully rebut it. The meaning of generic sentences is such that they can be true in several different ways. As a result, a speaker who is challenged after asserting a (...) class='Hi'>generic stereotype can often simply dismiss the objection and maintain that the stereotype is true in a way that is compatible with the challenger’s objection. In this paper, a semantic theory for generics is presented that accounts for this type of defensive shifting in upholding generic stereotypes. This theory is then used to develop two strategies to object more efficiently. The first strategy is to immediately deny that either of the two possible ways in which a generic can be true obtains. The second strategy is to deny the satisfaction of an additional condition that is necessary for a generic sentence to be true. (shrink)

We are often justified in acting on the basis of evidential confirmation. I argue that such evidence supports belief in non-quantificational generic generalizations, rather than universally quantified generalizations. I show how this account supports, rather than undermines, a Bayesian account of confirmation. Induction from confirming instances of a generalization to belief in the corresponding generic is part of a reasoning instinct that is typically (but not always) correct, and allows us to approximate the predictions that formal epistemology would (...) make. (shrink)

Generic statements (e.g., “Birds lay eggs”) express generalizations about categories. In this paper, we hypothesized that there is a paradoxical asymmetry at the core of generic meaning, such that these sentences have extremely strong implications but require little evidence to be judged true. Four experiments confirmed the hypothesized asymmetry: Participants interpreted novel generics such as “Lorches have purple feathers” as referring to nearly all lorches, but they judged the same novel generics to be true given a wide range (...) of prevalence levels (e.g., even when only 10% or 30% of lorches had purple feathers). A second hypothesis, also confirmed by the results, was that novel generic sentences about dangerous or distinctive properties would be more acceptable than generic sentences that were similar but did not have these connotations. In addition to clarifying important aspects of generics’ meaning, these findings are applicable to a range of real-world processes such as stereotyping and political discourse. (shrink)

The generic pronoun 'one' (or its empty counterpart, arbitrary PRO) exhibits a range of properties that show a special connection to the first person, or rather the relevant intentional agent (speaker, addressee, or described agent). The paper argues that generic 'one' involves generic quantification in which the predicate is applied to a given entity ‘as if’ to the relevant agent himself. This is best understood in terms of simulation, a central notion in some recent developments in the (...) philosophy of mind and cognitive science (Simulation Theory). (shrink)

When thinking about the notion of essence or of an essential feature, philosophers typically focus on what I will call the notion of objectual essence. The main aim of this paper is to argue that beside this familiar notion stands another one, the notion of generic essence, which contrary to appearance cannot be understood in terms of the familiar notion, and which also fails to be correctly characterized by certain other accounts which naturally come to mind as well. Some (...) of my objections to these accounts are similar to some of Kit Fine’s compelling objections to the standard modal account of (objectual) essence (Fine 1994). In the light of these objections, Fine advances the view that it is metaphysical necessity which has to be understood in terms of essence, rather than the other way around, and takes essence to be unanalyzable. When formulatinghis view, Fine had only objectual essence in mind (or had both concepts in mind, but assumed that the generic is a special case of the objectual), and for that reason, I will argue, his account fails. I will suggest that Fineans should modify their view, and take it that metaphysical necessity is to be understood in terms of the two notions of essence—a view I myself find appealing. Finally, I will end by suggesting a further move which reduces the objectual to the generic, making metaphysical necessity reducible to generic essence alone—a move with which I myself have some sympathy. (shrink)

The project of this paper is to deliver a semantics for a broad subset of bare plural generics about racial kinds, a class which I will dub 'Type C generics.' Examples include 'Blacks are criminal' and 'Muslims are terrorists.' Type C generics have two interesting features. First, they link racial kinds with ​ socially perspectival predicates ​ (SPPs). SPPs lead interpreters to treat the relationship between kinds and predicates in generic constructions as nomic or non-accidental. Moreover, in computing their (...) content, interpreters must make implicit reference to socially privileged​ ​ perspectives which are treated as authoritative about whether a given object fits into the extension of the predicate. Such deference grants these authorities influence over both the conventional meaning of these terms and over the nature of the ​ objects ​ in the social ontology that these terms purport to describe, much the way a baseball umpire is authoritative over the meaning and metaphysics of 'strike'/​ strike ​. Second, terms like 'criminal' and 'terrorist' receive default ​ racialized ​ interpretations in which these terms conventionally token racial or ethnic identities. I show that neither of these features can be explained by Sarah-Jane Leslie's influential 'weak semantics' for generics, and show how my own 'socially perspectival semantics' fares better on both counts. Finally, I give an analysis of 'Blacks are criminal' which explores the semantic mechanisms that underlie default racialized interpretations. (shrink)

A polynomial time ultrapower is a structure given by the set of polynomial time computable functions modulo some ultrafilter. They model the universal theory \ of all polynomial time functions. Generalizing a theorem of Hirschfeld :111–126, 1975), we show that every countable model of \ is isomorphic to an existentially closed substructure of a polynomial time ultrapower. Moreover, one can take a substructure of a special form, namely a limit polynomial time ultrapower in the classical sense of Keisler Ultrafilters across (...) mathematics, contemporary mathematics vol 530, pp 163–179. AMS, New York, 1963). Using a polynomial time ultrapower over a nonstandard Herbrand saturated model of \ we show that \ is consistent with a formal statement of a polynomial size circuit lower bound for a polynomial time computable function. This improves upon a recent result of Krajíček and Oliveira, 2017). (shrink)

We study notions of genericity in models of, inspired by lines of inquiry initiated by Chatzidakis and Pillay and continued by Dolich, Miller and Steinhorn in general model‐theoretic contexts. These papers studied the theories obtained by adding a “random” predicate to a class of structures. Chatzidakis and Pillay axiomatized the theories obtained in this way. In this article, we look at the subsets of models of which satisfy the axiomatization given by Chatzidakis and Pillay; we refer to these subsets in (...) models of as CP‐generics. We study a more natural property, called strong CP‐genericity, which implies CP‐genericity. We use an arithmetic version of Cohen forcing to construct (strong) CP‐generics with various properties, including ones in which every element of the model is definable in the expansion, and, on the other extreme, ones in which the definable closure relation is unchanged. (shrink)

I contrast two approaches to the interpretation of generics such as ‘ravens are black:’ majority-based views, on which they are about what is the case most of the time, and inquiry-based views, on which they are about a feature we focus on in inquiry. I argue that majority-based views face far more systematic counterexamples than has previously been supposed. They cannot account for generics about kinds with multiple characteristic properties, such as ‘elephants live in Africa and Asia.’ I then go (...) on to sketch an inquiry-based view. (shrink)

Our knowledge about the world is often expressed by generic sentences, yet their meanings are far from clear. This book provides answers to central problems concerning generics: what do they mean? Which factors affect their interpretation? How can one reason with generics? Cohen proposes that the meanings of generics are probability judgments, and shows how this view accounts for many of their puzzling properties, including lawlikeness. Generics are evaluated with respect to alternatives. Cohen argues that alternatives are induced by (...) the kind as well as by the predicated property, and thus provides a uniform account of the varied interpretations of generics. He studies the formal properties of alternatives and provides a compositional account of their derivation by focus and presupposition. Cohen uses his semantics of generics to provide a formal characterization of adequate default reasoning, and proves some desirable results of this formalism. (shrink)

What is the relationship between the claim that generics articulate psychologically primitive generalizations and the claim that they exhibit a unique form of context sensitivity? This paper maintains that the two claims are compatible. It develops and defends an overlooked form of contextualism grounded in the idiosyncrasies of System 1 thought.

Generics (e.g., “Ravens are black”) express generalizations about categories or their members. Previous research found that generics about animals are interpreted as broadly true of members of a kind, yet also accepted based on minimal evidence. This asymmetry is important for suggesting a mechanism by which unfounded generalizations may flourish; yet, little is known whether this finding extends to generics about groups of people (heretofore, “social generics”). Accordingly, in four preregistered studies (n = 665), we tested for an inferential asymmetry (...) for generics regarding novel groups of animals versus people. Participants were randomly assigned to either an Implied Prevalence task (given a generic, asked to estimate the prevalence of a property) or a Truth-Conditions task (given prevalence information, asked whether a generic was true or false). A generic asymmetry was found in both domains, at equivalent levels. The asymmetry also extended to properties varying in valence (dangerous and neutral). Finally, there were differences as a function of property valence in the Implied Prevalence task and a small but consistent interaction between domain and prevalence in the Truth-Conditions task. We discuss the implications of these results for the semantics of generics, theoretical accounts of the asymmetry, and the relation between generics and stereotyping. (shrink)

Generics are exception-admitting generalisations, which find expression in apparently diverse linguistic forms. A standard claim is that there is a hidden linguistic unity to genericity in the form of a covert operator, Gen. This article surveys and rejects a range of considerations that purport to show Gen to be syntactically essential to the explanation of a range of linguistic phenomena connected to genericity. The conclusion reached is that genericity is not a specifically linguistic property insofar as it does not supervene (...) upon any especial linguistic device; rather, genericity supervenes on broader cognitive competencies within linguistic constraints. (shrink)

The Ultrapower Axiom is an abstract combinatorial principle inspired by the fine structure of canonical inner models of large cardinal axioms. In this paper, it is established that the Ultrapower A...

The Ultrapower Axiom is an abstract combinatorial principle inspired by the fine structure of canonical inner models of large cardinal axioms. In this paper, it is established that the Ultrapower A...

Ducks lay eggs' is a true sentence, and `ducks are female' is a false one. Similarly, `mosquitoes carry the West Nile virus' is obviously true, whereas `mosquitoes don't carry the West Nile virus' is patently false. This is so despite the egg-laying ducks' being a subset of the female ones and despite the number of mosquitoes that don't carry the virus being ninety-nine times the number that do. Puzzling facts such as these have made generic sentences defy adequate semantic (...) treatment. However complex the truth conditions of generics appear to be, though, young children grasp generics more quickly and readily than seemingly simpler quantifiers such as `all' and `some'. I present an account of generics that not only illuminates the strange truth conditions of generics, but also explains how young children find them so comparatively easy to acquire. I then argue that generics give voice to our most cognitively primitive generalizations and that this hypothesis accounts for a variety of facts ranging from acquisition patterns to cross-linguistic data concerning the phonological articulation of operators. I go on to develop an account of the nature of these cognitively fundamental generalizations and argue that this account explains the strange truth-conditional behavior of generics. (shrink)

This paper is about an underappreciated aspect of generics: their non-specificity. Many uses of generics, utterances like ‘Seagulls swoop down to steal food’, express non-specific generalisations which do not specify their quantificational force or flavour. I consider whether this non-specificity arises as a by-product of context-sensitivity or semantic incompleteness but argue instead that generics semantically express non-specific generalisations by default as a result of quantifying existentially over more specific ones.

Let T be a model-complete theory that eliminates the quantifier $\exists^\infty x$ . For T we construct a theory T+ such that any element in a model of T+ determines a model of T. We show that T+ has a model companion T1. We can iterate the construction. The produced theories are investigated.

A prevailing thought is that generics have a covert modal operator at logical form. I claim that if this is right, the covert generic modality is a weak necessity modal. In this paper, I pr...

Are sagging pants cool? Are cows food? Are women more submissive than men? Are blacks more criminal than whites? Taking the social world at face value, many people would be tempted to answer these questions in the affirmative. And if challenged, they can point to facts that support their answers. But there is something wrong about the affirmative answers. In this chapter, I draw on recent ideas in the philosophy of language and metaphysics to show how the assertion of a (...) generic claim of the sort in question ordinarily permits one to infer that the fact in question obtains by virtue of something specifically about the subject so described, i.e., about women, or blacks, or sagging pants. In the examples I’ve offered, however, this implication inference is unwarranted. The facts in question obtain by virtue of broad system of social relations within which the subjects are situated, and are not grounded in intrinsic or dispositional features of the subjects themselves. The background relations are obscured, however, and as a result, the assertion is at least systematically misleading; a denial functions to block the problematic implication. Revealing such implications or presuppositions and blocking them is a crucial part of ideology critique. (shrink)

This paper is concerned with the semantics of bare plural I-generics such as ‘Tigers are striped’, ‘Chickens lay eggs’, and ‘Kangaroos live in Australia’. In a series of recent papers, Bernhard Nickel has developed a comprehensive view of a certain class of bare plural I-generics, which he calls characterizing sentences :629–648, 2009. doi:10.1007/s10988-008-9049-7; Linguist Philos 33:479–512, 2010a. doi:10.1007/s10988-011-9087-4; Philos Impr 10:1–25, 2010b). Nickel’s ambitious proposal includes a detailed account of their truth-conditions, an account of certain pragmatic phenomena that they give (...) rise to, a metaphysical picture of their truth-makers in terms of mechanisms, and an epistemological story connecting characterizing sentences to such concepts as induction and explanation. This paper offers an extended critique of the central truth-conditional component of Nickel’s proposal. In a nutshell, his account has it that ‘Tigers are striped’ is true iff, for tigers, there is a way of being normal with respect to fur-pattern such that all tigers that are normal that way are striped. I begin by explaining what characterizing sentences are and distinguish several readings that are available for sentences with bare plurals in subject position. I then introduce Nickel’s account and discuss some of its predictions which, in my view, seem highly problematic. Moreover, I argue that Nickel’s principle of Homogeneity does not go together well with his proposed truth-conditions, and that his truth-conditional account violates a plausible principle about the logic of generics, a principle I call generic non-contradiction. (shrink)