Moral and social philosophers often assume that humans beings are and ought to be autonomous. This tradition of individualism, or atomism, underlies many of our assumptions about ethics and law; it provides a legitimating framework for liberal democracy and free market capitalism. In this powerful book, David Weissman argues against atomistic ontologies, affirming instead that all of reality is social. Every particular is a system created by the reciprocal causal relations of its parts, he explains. Weissman formulates (...) an original metaphysics of nature that remains true to what is known through the empirical sciences, and he applies his hypothesis to a range of topics in psychology, morals, sociology, and politics. The author contends that systems are sometimes mutually independent, but many systems-human ones especially-are joined in higher order systems, such as families, friendships, businesses, and states, that are overlapping or nested. Weissman tests this schematic claim with empirical examples in chapters on persons, sociality, and value. He also considers how the scheme applies to particular issues related to deliberation, free speech, conflict, and ecology. (shrink)

Descartes' ideas not only changed the course of Western philosophy but also led to or transformed the fields of metaphysics, epistemology, physics and mathematics, political theory and ethics, psychoanalysis, and literature and the arts. This book reprints Descartes' major works, _Discourse on Method_ and _Meditations_, and presents essays by leading scholars that explore his contributions in each of those fields and place his ideas in the context of his time and our own. There are chapters by David Weissman (...) on metaphysics and psychoanalysis, John Post on epistemology, Lou Massa on physics and mathematics, William T. Bluhm on politics and ethics, and Thomas Pavel on literature and art. These essays are accompanied by others by David Weissman and by Stephen Toulmin that introduce the idea of intellectual lineages, discuss the period in which Descartes wrote, and reexamine the premises of his philosophy in light of contemporary philosophical, political, and social thinking. (shrink)

Traditional moral theory usually has either of two emphases: virtuous moral character or principles for distributing duties or goods. “Zone morality” introduces a third: families and businesses are systems created by the causal reciprocities of their members. These relations embody the duties and permissions of a system's moral code. Core systems satisfy basic interests and needs; we move easily among them, hardly noticing that moral demands vary from system to system. Moral conflicts arise because of discord within or among systems (...) but also because morality has three competing sites: personal attitudes and practices (benevolence or hostility), the moral codes of systems, and regulative principles that enhance social cohesion. A strong church or central government reduces conflict by imposing its rules. A democracy responds by encouraging persons and systems to participate in forums where claims are made; it promises fairness by requiring that all satisfy its legal procedures. (shrink)

Is something true because we believe it to be so or because it is true? How can a culturally bound community achieve scientific knowledge when values, attitudes, and desires shape its beliefs? In this book an eminent philosopher considers various schools of thought on the nature of truth. David Weissman argues that truth exists in the correspondence between statement and fact: what can be said about our world can be measured against a reality that has a character and (...) existence independent of any property we ascribe to it. Weissman begins by evaluating the transcendental paradigm of Kant that has exercised enormous influence in the development of Western thought over the past two hundred years. He develops his critique of the Kantian model, in which value judgments underlie the perception or construction of truth, asserting that it is seriously flawed because it renders a determination of truth impossible. Weissman examines various value-driven perspectives on truth developed by such philosophers as Foucault, Derrida, and Rorty, for whom truth is only the set of affirmations, principles, and procedures sanctioned by power and value. However, says Weissman, truth is the required adjunct to desire. Knowing who we are, where we have been, and the consequences of what we have done is the essential preparation for choosing what to do next. We must respect the integrity of a world we have not made and find our way within it with the help of attitudes and desires that have been informed by truth. (shrink)

We often read Plato’s cave allegory for its trajectory: out of darkness into light. The back of the cave—where imagination projects fantasies onto shadows—is a place to flee. This part of the allegory reduces reality testing to thought or imagining, ignoring action and the people or things engaged. Yet thinkers prominent in our time—Immanuel Kant and W. V. O. Quine—suppose that our experience of the world is that of the cave’s prisoners: we too mistake fantasies for reality. This is an (...) odd stance when practical life and science—beliefs informed by action and experiment—are better tests of reality than their arguments for world‐making. (shrink)

Metaphysics is the inquiry having categorial form as its aim. Once all but defunct, metaphysics has now revived, though without disciplinary focus. Nine points of entry dominate current studies, each separate from and largely oblivious to the others. This essay characterizes the nine, expressing its preference for a discipline grounded in the empirical sciences while pursuing issues they ignore.

Philosophical examination of the relationship of normativity and freedom.

Recognition of the harms done by free speech is a function of the social ontology presupposed. An atomist ontology implies that the harms suffered are restricted to individual people. This paper suggests an alternate ontology—one that describes systems established by the causal reciprocities of their proper parts. It proposes a consequentialist moral theory, and considers the harms suffered by these systems when speech exposes their internal, otherwise private, behaviors or features, when speech is malicious and false, and when speech is (...) monopolistic. Does the proposed ontology have objectionable implications for public policy? Alternative answers are considered briefly. (shrink)

The Lévy-Solovay Theorem [8] limits the kind of large cardinal embeddings that can exist in a small forcing extension. Here I announce a generalization of this theorem to a broad new class of forcing notions. One consequence is that many of the forcing iterations most commonly found in the large cardinal literature create no new weakly compact cardinals, measurable cardinals, strong cardinals, Woodin cardinals, strongly compact cardinals, supercompact cardinals, almost huge cardinals, huge cardinals, and so on.

I consider the natural infinitary variations of the games Wordle and Mastermind, as well as their game‐theoretic variations Absurdle and Madstermind, considering these games with infinitely long words and infinite color sequences and allowing transfinite game play. For each game, a secret codeword is hidden, which the codebreaker attempts to discover by making a series of guesses and receiving feedback as to their accuracy. In Wordle with words of any size from a finite alphabet of n letters, including infinite words (...) or even uncountable words, the codebreaker can nevertheless always win in n steps. Meanwhile, the mastermind number, defined as the smallest winning set of guesses in infinite Mastermind for sequences of length ω over a countable set of colors without duplication, is uncountable, but the exact value turns out to be independent of, for it is provably equal to the eventually different number, which is the same as the covering number of the meager ideal. I thus place all the various mastermind numbers, defined for the natural variations of the game, into the hierarchy of cardinal characteristics of the continuum. (shrink)

ONE ASSUMPTION ABOUT METAPHYSICS is often shared by those who renounce it. Metaphysical theories are not true, they say, because of being neither true nor false. Opponents of one sort excoriate the theories as meaningless. Others say that truth and falsity are irrelevant to metaphysics, as they are to literature. Like novelists and playwrights, we metaphysicians are said to formulate the stories used for thinking about possible worlds, such as the imaginary ones of fiction and this actual world. Metaphysics, this (...) implies, differs from literature only because its stories have a wider scope. Where novelists devote themselves to incidents and personalities, we metaphysicians tell stories that emphasize the categorial features of a world. Either way, these activities are motivated by a single objective: we formulate interpretations in order to use them for creating thinkable worlds. All of the intelligibility credited to any possible world--all its differentiations and relations--originate within these interpretations. But no one should suppose that interpretations are true or false; for these conceptualizations are not the representations of preexisting states of affairs. They are, instead, the very condition for the existence of possible worlds. Why? Because these worlds exist only as they are prefigured within, and created by, the interpretations used for thinking them. (shrink)

We present several generalizations of the well-known Kunen inconsistency that there is no nontrivial elementary embedding from the set-theoretic universe V to itself. For example, there is no elementary embedding from the universe V to a set-forcing extension V[G], or conversely from V[G] to V, or more generally from one set-forcing ground model of the universe to another, or between any two models that are eventually stationary correct, or from V to HOD, or conversely from HOD to V, or indeed (...) from any definable class to V, among many other possibilities we consider, including generic embeddings, definable embeddings and results not requiring the axiom of choice. We have aimed in this article for a unified presentation that weaves together some previously known unpublished or folklore results, several due to Woodin and others, along with our new contributions. (shrink)

We introduce the $\Sigma _1$ -definable universal finite sequence and prove that it exhibits the universal extension property amongst the countable models of set theory under end-extension. That is, the sequence is $\Sigma _1$ -definable and provably finite; the sequence is empty in transitive models; and if M is a countable model of set theory in which the sequence is s and t is any finite extension of s in this model, then there is an end-extension of M to a (...) model in which the sequence is t. Our proof method grows out of a new infinitary-logic-free proof of the Barwise extension theorem, by which any countable model of set theory is end-extended to a model of $V=L$ or indeed any theory true in a suitable submodel of the original model. The main theorem settles the modal logic of end-extensional potentialism, showing that the potentialist validities of the models of set theory under end-extensions are exactly the assertions of S4. Finally, we introduce the end-extensional maximality principle, which asserts that every possibly necessary sentence is already true, and show that every countable model extends to a model satisfying it. (shrink)

In_ Dispositional Properties_, David Weissman attacks a problem central to the philosophy of mind and, by implication, to the theory of being: Are there potentialities, capabilities, which dispose the mind to think in one way rather than another? The volume is arranged in the form of four arguments that converge upon a single point. First, there is an intricate discussion of the shortcomings of Hume's account of mind as ideas and impressions. Next comes a brief treatment of the (...) arguments of some of Weissman's contemporaries, including Carnap and Braithwaite. Third, Weissman discusses Wittgenstein's theories of learning and knowledge. Finally, there is a full discussion of Aristotle and his doctrine of potentialities. The question this book ultimately raises is how to steer between a doctrine of mind as no more than a series of acts, on the one hand, and a doctrine of mind as a kind of unitary object, on the other. The solution is to show first of all that there must be a potentiality in the universe, and then to show clearly and in detail that the mind is shot through with that potentiality. __. (shrink)

The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous range of set-theoretic possibilities, a phenomenon that challenges the universe (...) view. In particular, I argue that the continuum hypothesis is settled on the multiverse view by our extensive knowledge about how it behaves in the multiverse, and as a result it can no longer be settled in the manner formerly hoped for. (shrink)

A pointwise definable model is one in which every object is \loos definable without parameters. In a model of set theory, this property strengthens $V=\HOD$, but is not first-order expressible. Nevertheless, if \ZFC\ is consistent, then there are continuum many pointwise definable models of \ZFC. If there is a transitive model of \ZFC, then there are continuum many pointwise definable transitive models of \ZFC. What is more, every countable model of \ZFC\ has a class forcing extension that is pointwise definable. (...) Indeed, for the main contribution of this article, every countable model of Gödel-Bernays set theory has a pointwise definable extension, in which every set and class is first-order definable without parameters. (shrink)

A sequel to Weissman's Intuition and ideality (1987).

Using the lottery preparation, we prove that any strongly unfoldable cardinal $\kappa$ can be made indestructible by all.

We introduce the resurrection axioms, a new class of forcing axioms, and the uplifting cardinals, a new large cardinal notion, and prove that various instances of the resurrection axioms are equiconsistent over ZFC with the existence of an uplifting cardinal.

We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and Löwe [14], including the use of buttons, switches, dials and ratchets. Among the potentialist conceptions we consider are: rank potentialism, Grothendieck–Zermelo potentialism, transitive-set potentialism, forcing potentialism, countable-transitive-model potentialism, countable-model potentialism, and others. In each case, we identify lower bounds for the modal validities, which are generally either S4.2 or S4.3, (...) and an upper bound of S5, proving in each case that these bounds are optimal. The validity of S5 in a world is a potentialist maximality principle, an interesting set-theoretic principle of its own. The results can be viewed as providing an analysis of the modal commitments of the various set-theoretic multiverse conceptions corresponding to each potentialist account. (shrink)

In the Tractatus Wittgenstein espouses a theory of mind and knowledge that is like Plato’s: he exhibits the theory as he argues that propositional signs picture states of affairs. That is the conclusion for which I shall argue in this paper.

The lottery preparation, a new general kind of Laver preparation, works uniformly with supercompact cardinals, strongly compact cardinals, strong cardinals, measurable cardinals, or what have you. And like the Laver preparation, the lottery preparation makes these cardinals indestructible by various kinds of further forcing. A supercompact cardinal κ, for example, becomes fully indestructible by <κ-directed closed forcing; a strong cardinal κ becomes indestructible by κ-strategically closed forcing; and a strongly compact cardinal κ becomes indestructible by, among others, the forcing to (...) add a Cohen subset to κ, the forcing to shoot a club Cκ avoiding the measurable cardinals and the forcing to add various long Prikry sequences. The lottery preparation works best when performed after fast function forcing, which adds a new completely general kind of Laver function for any large cardinal, thereby freeing the Laver function concept from the supercompact cardinal context. (shrink)

After reviewing various natural bi-interpretations in urelement set theory, including second-order set theories with urelements, we explore the strength of second-order reflection in these contexts. Ultimately, we prove, second-order reflection with the abundant atom axiom is bi-interpretable and hence also equiconsistent with the existence of a supercompact cardinal. The proof relies on a reflection characterization of supercompactness, namely, a cardinal κ is supercompact if and only if every Π11 sentence true in a structure M (of any size) containing κ in (...) a language of size less than κ is also true in a substructure m≺M of size less than κ with m∩κ∈κ. (shrink)

We introduce the subject of modal model theory, where one studies a mathematical structure within a class of similar structures under an extension concept that gives rise to mathematically natural notions of possibility and necessity. A statement φ is possible in a structure (written φ) if φ is true in some extension of that structure, and φ is necessary (written φ) if it is true in all extensions of the structure. A principal case for us will be the class Mod(T) (...) of all models of a given theory T—all graphs, all groups, all fields, or what have you—considered under the substructure relation. In this article, we aim to develop the resulting modal model theory. The class of all graphs is a particularly insightful case illustrating the remarkable power of the modal vocabulary, for the modal language of graph theory can express connectedness, k-colorability, finiteness, countability, size continuum, size ℵ1, ℵ2, ℵω, ℶω, first ℶ-fixed point, first ℶ-hyper-fixed point, and much more. A graph obeys the maximality principle φ(a)→φ(a) with parameters if and only if it satisfies the theory of the countable random graph, and it satisfies the maximality principle for sentences if and only if it is universal for finite graphs. (shrink)

We consider a set-theoretic version of mereology based on the inclusion relation ⊆ and analyze how well it might serve as a foundation of mathematics. After establishing the non-definability of ∈ from ⊆, we identify the natural axioms for ⊆-based mereology, which constitute a finitely axiomatizable, complete, decidable theory. Ultimately, for these reasons, we conclude that this form of set-theoretic mereology cannot by itself serve as a foundation of mathematics. Meanwhile, augmented forms of set-theoretic mereology, such as that obtained by (...) adding the singleton operator, are foundationally robust. (shrink)

This book is an explication and defense of the author's modal realism. There are possible worlds and individuals, he says, different from the possibles realized in this world of ours. The reality of the many possibilities is a hypothesis needed for explaining the representational character of our language, as when we say that there might be talking donkeys, though there are none. It is the reality of these possibles, as worlds and individuals, that Lewis defends.

Philosophic attention shifted after Hegel from Kant's emphasis on sensibility to criticism and analyses of the fine arts. The arts themselves seemed as ample as nature; a disciplined science could devote as much energy to one as the other. But then the arts began to splinter because of new technologies: photography displaced figurative painting; hearing recorded music reduced the interest in learning to play it. The firm interiority that Hegel assumed was undermined by the speed, mechanization, and distractions of modern (...) life. We inherit two problems: restore quality and conviction in the arts; cultivate the interiority--the sensibility--that is a condition for judgment in every domain. What is sensibility's role in experiences of every sort, but especially those provoked when art is made and enjoyed? (shrink)

The main theorem of this article is that every countable model of set theory 〈M, ∈M〉, including every well-founded model, is isomorphic to a submodel of its own constructible universe 〈LM, ∈M〉 by means of an embedding j : M → LM. It follows from the proof that the countable models of set theory are linearly pre-ordered by embeddability: if 〈M, ∈M〉 and 〈N, ∈N〉 are countable models of set theory, then either M is isomorphic to a submodel of N (...) or conversely. Indeed, these models are pre-well-ordered by embeddability in order-type exactly ω1+ 1. Specifically, the countable well-founded models are ordered under embeddability exactly in accordance with the heights of their ordinals; every shorter model embeds into every taller model; every model of set theory M is universal for all countable well-founded binary relations of rank at most OrdM; and every ill-founded model of set theory is universal for all countable acyclic binary relations. Finally, strengthening a classical theorem of Ressayre, the proof method shows that if M is any nonstandard model of PA, then every countable model of set theory — in particular, every model of ZFC plus large cardinals — is isomorphic to a submodel of the hereditarily finite sets 〈 HFM, ∈M〉 of M. Indeed, 〈 HFM, ∈M〉 is universal for all countable acyclic binary relations. (shrink)

An introduction to writing proofs, presented through compelling mathematical statements with interesting elementary proofs. This book offers an introduction to the art and craft of proof-writing. The author, a leading research mathematician, presents a series of engaging and compelling mathematical statements with interesting elementary proofs. These proofs capture a wide range of topics, including number theory, combinatorics, graph theory, the theory of games, geometry, infinity, order theory, and real analysis. The goal is to show students and aspiring mathematicians how to (...) write proofs with elegance and precision. (shrink)