This essay is written in two parts. The first is a commentary on the affective politics of philosophy as a discipline. The theme here is philosophy’s reverence problem, an affective bond to the teacher and the text, which is threatened or even injured by feminist philosophy. Feminist philosophy emerges as disruptive irreverence in the midst of the discipline, and injured reverence becomes a powerful prereflective motivation for resistance to feminist thought. The second part of the essay is an exploration of (...) the field of inquiry called feminist phenomenology. Is feminist phenomenology simply phenomenology from another point of view, that of the embodied female subject? Is it conducted, in other words, in a space beyond politics and power where the difference of this subject discloses values and meanings that have not yet been thematized in phenomenological inquiry, but which phenomenology is already competent to pursue? Or does feminist phenomenology disrupt or transform phenomenological practice as we traditionally understand it? In this paper, I claim that phenomenology must be critical in order to be feminist, that it must disrupt phenomenological practice rather than simply “applying” it to a new object, “woman.” In the work of Simone de Beauvoir we find a different phenomenological practice that feminists can count as a positive inheritance. The real difference of feminist phenomenology, however, only emerges in the practice itself. In order to capture something about this difference I take the phenomenon of shame as a case study, and compare three recent phenomenological accounts of shame. (shrink)

Bringing together 20 foundational texts in contemporary modernist criticism in one accessible volume, this book explores the debates that have transformed the field of modernist studies at the turn of the millennium and into the 21st century. The New Modernist Studies Reader features chapters covering the major topics central to the study of modernism today, including: Feminism, gender and sexuality; Empire and race; Print and media cultures; Historical and geographical debates. Each text includes an introductory summary of its historical and (...) intellectual contexts, as well as guides to further reading to help students and teachers explore the ideas further. Includes essential texts by leading critics such as: Pascale Casanova, Anne Anlin Cheng, Brent Hayes Edwards, Rita Felski, Susan Stanford Friedman, Mark Goble, Miriam Hansen, Andreas Huyssen, David James, Fredric Jameson, Heather K. Love, Douglas Mao, Mark S. Morrisson, Michael North, Jessica Pressman, Lawrence Rainey, Paul K. Saint-Amour, Bonnie Kime Scott, Urmila Seshagiri, Robert Spoo, and Rebecca Walkowitz. (shrink)

There has been much discussion about whether traditional epistemology's doxastic attitudes are reducible to degrees of belief. In this paper I argue that what I call the Straightforward Reduction - the reduction of all three of believing p, disbelieving p, and suspending judgment about p, not-p to precise degrees of belief for p and not-p that ought to obey the standard axioms of the probability calculus - cannot succeed. By focusing on suspension of judgment (agnosticism) rather than belief, we can (...) see why the Straightforward Reduction is bound to fail. I argue that, in general, suspending about p is not just a matter of having some specified standard credence for p, and in the end I suggest some ways to extend the arguments that will put pressure on other credence-theoretic accounts of belief and suspension of judgment as well. (shrink)

Capitalism is the best. It's free enterprise. Barter. Gimbels, if I get really rank with the clerk, 'Well I don't like this', how I can resolve it? If it really gets ridiculous, I go, 'Frig it, man, I walk.' What can this guy do at Gimbels, even if he was the president of Gimbels? He can always reject me from that store, but I can always go to Macy's. He can't really hurt me. Communism is like one big phone company. (...) Government control, man. And if I get too rank with that phone company, where can I go? I'll end up like a schmuck with a dixie cup on a thread. (shrink)

Rudolf Carnap is increasingly regarded as one of the most important philosophers of the twentieth century. He was one of the leading figures of the logical empiricist movement associated with the Vienna Circle and a central figure in the analytic tradition more generally. He made major contributions to philosophy of science and philosophy of logic, and, perhaps most importantly, to our understanding of the nature of philosophy as a discipline. In this volume a team of contributors explores the major themes (...) of his philosophy and discusses his relationship with the Vienna Circle and with philosophers such as Frege, Husserl, Russell, and Quine. New readers will find this the most convenient and accessible guide to Carnap currently available. Advanced students and specialists will find a conspectus of recent developments in the interpretation of Carnap. (shrink)

Scientific disagreements are an important catalyst for scientific progress. But what happens when scientists disagree amidst times of crisis, when we need quick yet reliable policy guidance? In this paper we provide a normative account for how scientists facing disagreement in the context of ‘fast science’ should respond, and how policy makers should evaluate such disagreement. Starting from an argumentative, pragma-dialectic account of scientific controversies, we argue for the importance of ‘higher-order evidence’ (HOE) and we specify desiderata for scientifically relevant (...) HOE. We use our account to analyze the controversy about the aerosol transmission of COVID-19. (shrink)

Historians of philosophy, science, and mathematics explore the influence of Kant's philosophy on the evolution of modern scientific thought.

Reflection, in the sense of [Fr03a] and [Fr03b], is based on the idea that a category of classes has a subclass that is “similar” to the category. Here we present axiomatizations based on the idea that a category of classes that does not form a class has extensionally different subclasses that are “similar”. We present two such similarity principles, which are shown to interpret and be interpretable in certain set theories with large cardinal axioms.

In this panel, we explore the future of value sensitive design (VSD). The stakes are high. Many in public and private sectors and in civil society are gradually realizing that taking our values seriously implies that we have to ensure that values effectively inform the design of technology which, in turn, shapes people’s lives. Value sensitive design offers a highly developed set of theory, tools, and methods to systematically do so.

Better understanding the psychological factors related to certainty in one’s beliefs (i.e., dogmatism) has important consequences for both individuals and social groups. Generally, beliefs can find support from at least two different routes of information processing: social/moral considerations or analytic/empirical reasoning. Here, we investigate how these two psychological constructs relate to dogmatism in two groups of individuals who preferentially draw on the former or latter sort of information when forming beliefs about the world- religious and non religious individuals. Across two (...) studies and their pooled analysis, we provide evidence that although dogmatism is negatively related to analytic reasoning in both groups of individuals, it shares a divergent relationship with measures of moral concern depending on whether one identifies as religious or not. Study 1 showed that increasing levels of dogmatism were positively related to prosocial intentions among the religious and negatively related to empathic concern among the nonreligious. Study 2 replicated and extended these results by showing that perspective taking is negatively related to dogmatism in both groups, an effect which is particularly robust among the nonreligious. Study 2 also showed that religious fundamentalism was positively related to measures of moral concern among the religious. Because the current studies used a content neutral measure to assess dogmatic certainty in one’s beliefs, they have the potential to inform practices for most effectively communicating with and persuading religious and nonreligious individuals to change maladaptive behavior, even when the mode of discourse is unrelated to religious belief. (shrink)

Here we take the view that LPC(=) is applicable to structures whose domain is too large to be a set. This is not just a matter of class theory versus set theory, although it can be interpreted as such, and this interpretation is discussed briefly at the end.

We now fix A ⊆ Q. We study a fundamental class of digraphs associated with A, which we call the A-digraphs. An A,kdigraph is a digraph (Ak,E), where E is an order invariant subset of A2k in the following sense. For all x,y ∈ A2k, if x,y have the same order type then x ∈ E ↔ y ∈ E.

Loose, unconnected, free-floating, mobile: this is the modern individual, at least in comparison with the immediate past.

We consider a number of statements involving restrictions and extensions of algebras, and derive connections with large cardinal axioms.

The kind of unknowability I will discuss concerns the count of certain natural finite sets of objects. Even the situation with regard to our present strong formal systems is rather unclear. One can just profitably focus on that, putting aside issues of general unknowability.

We give a consistency proof within a weak fragment of arithmetic of elementary algebra and geometry. For this purpose, we use EFA (exponential function arithmetic), and various first order theories of algebraically closed fields and real closed fields.

Three-dimensional material models of molecules were used throughout the 19th century, either functioning as a mere representation or opening new epistemic horizons. In this paper, two case studies are examined: the 1875 models of van ‘t Hoff and the 1890 models of Sachse. What is unique in these two case studies is that both models were not only folded, but were also conceptualized mathematically. When viewed in light of the chemical research of that period not only were both of these (...) aspects, considered in their singularity, exceptional, but also taken together may be thought of as a subversion of the way molecules were chemically investigated in the 19th century. Concentrating on this unique shared characteristic in the models of van ‘t Hoff and the models of Sachse, this paper deals with the shifts and displacements between their operational methods and existence: between their technical and epistemological aspects and the fact that they were folded, which was forgotten or simply ignored in the subsequent development of chemistry. (shrink)

We present some examples of mathematically natural nonrecursive sets of integers and relations on integers by combining results from Part 1, recursion theory, and from the negative solution to Hilbert’s 10th Problem ([3], [1], and [2]).

An unprovable theorem is a mathematical result that can-not be proved using the com-monly accepted axioms for mathematics (Zermelo-Frankel plus the axiom of choice), but can be proved by using the higher infinities known as large cardinals. Large car-dinal axioms have been the main proposal for new axioms originating with Gödel.

An extreme kind of logic skeptic claims that "the present formal systems used for the foundations of mathematics are artificially strong, thereby causing unnecessary headaches such as the Gödel incompleteness phenomena". The skeptic continues by claiming that "logician's systems always contain overly general assertions, and/or assertions about overly general notions, that are not used in any significant way in normal mathematics. For example, induction for all statements, or even all statements of certain restricted forms, is far too general - mathematicians (...) only use induction for natural statements that actually arise. If logicians would tailor their formal systems to conform to the naturalness of normal mathematics, then various logical difficulties would disappear, and the story of the foundations of mathematics would look radically different than it does today. In particular, it should be possible to give a convincing model of actual mathematical practice that can be proved to be free of contradiction using methods that lie within what Hilbert had in mind in connection with his program”. Here we present some specific results in the direction of refuting this point of view, and introduce the Strict Reverse Mathematics (SRM) program. (shrink)

It has been accepted since the early part of the Century that there is no problem formalizing mathematics in standard formal systems of axiomatic set theory. Most people feel that they know as much as they ever want to know about how one can reduce natural numbers, integers, rationals, reals, and complex numbers to sets, and prove all of their basic properties. Furthermore, that this can continue through more and more complicated material, and that there is never a real problem.

We axiomatize EFA in strictly mathematical terms, involving only the ring operations, without extending the language by either exponentiation, finite sets of integers, or polynomials.

We can equivalently present this by the recursion equations f1(n) = 2n, fk+1(1) = fk(1), fk+1(n+1) = fk(fk+1(n)), where k,n ≥ 1. We define A(k,n) = fk(n).

In mathematics, we back up our discoveries with rigorous deductive proofs. Mathematicians develop a keen instinctive sense of what makes a proof rigorous. In logic, we strive for a *theory* of rigorous proofs.

Each of these theorems and concepts arose from very specific considerations of great general interest in the foundations of mathematics (f.o.m.). They each serve well defined purposes in f.o.m. Naturally, the preferred way to formulate them for mathe-matical logicians is in terms that are close to their roots in f.o.m.

We present several selection theorems for Borel relations, involving only Borel sets and functions, all of which can be obtained as consequences of closely related theorems proved in [DSR 96,99,01,01X] involving coanalytic sets. The relevant proofs given there use substantial set theoretic methods, which were also shown to be necessary. We show that none of our Borel consequences can be proved without substantial set theoretic methods. The results are established for Baire space. We give equivalents of some of the main (...) results for the reals. (shrink)

We give a complete proof that all 3 quantifier sentences in the primitive notation of set theory (Œ,=), are decided in ZFC, and in fact in a weak fragment of ZF without the power set axiom. We obtain information concerning witnesses of 2 quantifier formulas with one free variable. There is a 5 quantifier sentence that is not decided in ZFC (see [Fr02]).

We present two forms of “sentential reflection”, which are shown to be mutually interpretable with Z2 and ZFC, respectively.

A lot of the well known impact of the Gödel phenomena is in the form of painful messages telling us that certain major mathematical programs cannot be completed as intended. This aspect of Gödel – the delivery of bad news –is not welcomed, and defensive measures are now in place.

Mathematical statements arising from program verification are believed to be much easier to deal with than statements coming from serious mathematics. At least this is true for “normal programming”.

1. Transfer principles from N to On. A. Mahlo cardinals. B. Weakly compact cardinals. C. Ineffable cardinals. D. Ramsey cardinals. E. Ineffably Ramsey cardinals. F. Subtle cardinals. G. From N to (...) 4. Decidability of statements on N. 5. Decidability of statements on shrink)

This is widely accepted, inside and outside philosophy, but one can spend an entire career clarifying, justifying, and amplifying on this statement. Certainly a graduate student career.

Provide a formal system that is a conservative extension of PA for Π02 sentences, and even a conservative extension of HA, that supports the worry free smooth development of constructive analysis in the style of Errett Bishop.