The C3 Framework encourages ambitious inquiry-based social studies teaching. While inquiry is regularly recommended as a preferred pedagogy, research has shown that social studies teachers rarely engage students in inquiry. This exploratory study surveyed social studies teachers in one school district in a southeastern state to update our understanding of teachers’ instructional beliefs and practices related to inquiry and the C3 Framework. Survey responses were analyzed using descriptive statistics and open coding. Findings indicate that the majority of teachers use instructional (...) practices that may be supportive of the C3 Framework and that the ideas within the C3 Framework resonate with most respondents. At the same time, teachers reported challenges with some key concepts within the Framework, such as taking informed action in the classroom and using questions to initiate an inquiry. While the idea of inquiry as espoused by the C3 Framework resonated with teachers, the extent to which they both believe in and practice inquiry methods is unclear and necessitates further study. This study is an initial step to inform future research and efforts to implement the C3 Framework in K-12 social studies classrooms. (shrink)

Individuals typically produce auditory sequences, such as speech or music, at a consistent spontaneous rate or tempo. We addressed whether spontaneous rates would show patterns of convergence across the domains of music and language production when the same participants spoke sentences and performed melodic phrases on a piano. Although timing plays a critical role in both domains, different communicative and motor constraints apply in each case and so it is not clear whether music and speech would display similar timing mechanisms. (...) We report the results of two experiments in which adult participants produced sequences from memory at a comfortable spontaneous (uncued) rate. In Experiment 1, monolingual pianists in Buffalo, New York engaged in three production tasks: speaking sentences from memory, performing short melodies from memory, and tapping isochronously. In Experiment 2, English-French bilingual pianists in Montréal, Canada produced melodies on a piano as in Experiment 1, and spoke short rhythmically-structured phrases repeatedly. Both experiments led to the same pattern of results. Participants exhibited consistent spontaneous rates within each task. People who produced one spoken phrase rapidly were likely to produce another spoken phrase rapidly. This consistency across stimuli was also found for performance of different musical melodies. In general, spontaneous rates across speech and music tasks were not correlated, whereas rates of tapping and music were correlated. Speech rates (for syllables) were faster than music rates (for tones) and speech showed a smaller range of spontaneous rates across individuals than did music or tapping rates. Taken together, these results suggest that spontaneous rate reflects cumulative influences of endogenous rhythms (in consistent self-generated rates within domain), peripheral motor constraints (in finger movements across tapping and music), and communicative goals based on the cultural transmission of auditory information (slower rates for to-be-synchronized music than for speech). (shrink)

Both Morain and Largent (2023) and Garland, Morain, and Sugarman (2023) recognize the ethical challenges inherent in clinician participation in embedded research. Focusing on the question of integr...

This is the first book on Buber to address the full scope of his seminal influence for any number of thinkers and fields from philosophy to psychotherapy to literary theory.

Informal statements of Gödel's Second Incompleteness Theorem, referred to here as Informal Second Incompleteness, are simple and dramatic. However, current versions of Formal Second Incompleteness are complicated and awkward. We present new versions of Formal Second Incompleteness that are simple, and informally imply Informal Second Incompleteness. These results rest on the isolation of simple formal properties shared by consistency statements. Here we do not address any issues concerning proofs of Second Incompleteness.

This paper defends the Intention Account of Inquiry. On this account, inquiry is best understood by appeal to a ‘question-directed intention’ (QDI), an intention to answer a question broadly construed. This account’s core commitments help meet recent challenges plaguing extant approaches to characterizing inquiry. First, QDIs are the type of mental state central to inquiry, not attitudes like curiosity or wonder. Second, holding a QDI towards a question and acting in service of it constitutes the start of inquiry. Third, controversial (...) norms which mandate a rational inquirer's ignorance towards the answer to her question can be reformulated and defended by appeal to rational constraints on intention. Fourth, instrumental pressures inquirers face are the standard pressures of plan-rationality. In defending these theses, I show that the Intention Account provides compelling explanations to standing challenges, in ways competitors cannot. It does so by advancing understanding of how our epistemic and practical agency are intertwined. (shrink)

We characterize the classifiability of a countable first-order theory T in terms of the solvability of the potential-isomorphism problem for models of T.

This paper considers the evolution of the problem of scientific rationality from Kant through Carnap to Kuhn. I argue for a relativized and historicized version of the original Kantian conception of scientific a priori principles and examine the way in which these principles change and develop across revolutionary paradigm shifts. The distinctively philosophical enterprise of reflecting upon and contextualizing such principles is then seen to play a key role in making possible rational intersubjective communication between otherwise incommensurable paradigms.

What do we owe those with whom we inquire? Presumably, quite a bit. Anything beyond what is necessary to secure knowledge? Yes. In this paper, I argue for a class of ‘zetetic rights.’ These are rights distinctive to participants in group inquiry. Zetetic rights help protect important central interests of inquirers. These include a right to aid, a right against interference, and a right to exert influence over the course of inquiry. Building on arguments by Fricker (2015), I defend these (...) rights, and explore cases of their violation: zetetic wrongings. I argue that zetetic wrongings constitute a distinctive, ubiquitous, and significant form of injustice in our epistemic and zetetic lives. To improve our inquiries and avoid epistemic injustice, we need to contend with zetetic wronging. Making this case helps show that a complete picture of epistemic life must account for the deep influence of our cooperative ties to one another. (shrink)

The notion of interpretation is absolutely fundamental to mathematical logic and the foundations of mathematics. It is also crucial for the foundations and philosophy of science - although here some crucial conditions generally need to be imposed; e.g., “the interpretation leaves the mathematical concepts unchanged”.

Recent discussions of logical pluralism trace its origins to Rudolf Carnap’s principle of tolerance; indeed, the principle is seen as one of Carnap’s lasting philosophical contributions. In this paper, I will argue that Carnap’s reasons for adopting this principle are not purely logical, but are rather founded in the Vienna Circle’s manifesto—a programmatic document that brings the Circle’s philosophical work together with a program of social change. Building on work by Uebel, Romizi, and others, I argue that we must understand (...) the principle in light of Carnap’s role in writing the manifesto, and thus as integrated into the larger philosophical and political goals of the Circle. This history illuminates the often-ignored relationship between Carnap’s logical pluralism and his political views. Finally, I turn to the political situation of the post-World War 2 period in the United States. During this time, the Circle’s emigres in the USA transitioned their work from active efforts to reform society to the technical work that we recognize as the foundation of American analytic philosophy today. In this final section, I argue that the reasons that Carnap distanced himself from the political foundations of his view were due in large part to McCarthy-era persecution of left-wing academics. (shrink)

The use of x[y,z,w] rather than the more usual y Πx has many advantages for this work. One of them is that we have found a convenient way to eliminate any need for axiom schemes. All axioms considered are single sentences with clear meaning. (In one case only, the axiom is a conjunction of a manageable finite number of sentences).

A complex of transformations, carried into effect with varying tempos since the beginning of the era of industrial revolutions, has disrupted a certain number of human societies: societies which the ethnologists often call “modern” in opposing them to those labeled “traditional.”.

Russell’s way out of his paradox via the impre-dicative theory of types has roughly the same logical power as Zermelo set theory - which supplanted it as a far more flexible and workable axiomatic foundation for mathematics. We discuss some new formalisms that are conceptually close to Russell, yet simpler, and have the same logical power as higher set theory - as represented by the far more powerful Zermelo-Frankel set theory and beyond. END.

The title of this Festschrift to Stephen Brown points to the understanding of medieval philosophy and theology in the longue durée of their traditions and discourses.

An ideal in a commutative ring R with unit is a nonempty I Õ R such that for all x,y Œ I, z Œ R, we have x+y and xz Œ I. A set of generators for I is a subset of I such that I is the least ideal containing that subset.

If A is an admissible set, let HC(A) = {x∣ x ∈ A and x is hereditarily countable in A}. Then HC(A) is admissible. Corollaries are drawn characterizing the "real parts" of admissible sets and the analytical consequences of admissible set theory.

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.

The Borel reducibility theory of Polish equivalence relations, at least in its present form, was initiated independently in [FS89] and [HKL90]. There is now an extensive literature on this topic, including fundamental work on the Glimm-Effros dichotomy in [HKL90], on countable Borel equivalence relations in [DJK94], and on Polish group actions in [BK96].

The Complete Theory of Everything (CTE) is based on certain axioms of indiscernibility. Such axioms of indiscernibility have been given a philosophical justification by Kit Fine. I want to report on an attempt to give strong indiscernibility axioms which might also be subject to such philosophical analysis, and which prove the consistency of set theory; i.e., ZFC or more. In this way, we might obtain a (new kind of) philosophical consistency proof for mathematics.

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.

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.

In How States Think, John Mearsheimer and Sebastian Rosato argue that expected-utility maximization is too subjective to serve as the basis for making rational decisions in the realm of national security. They claim that rationality in security studies should instead be defined by whether leaders conduct deliberative, theory-driven reasoning. This essay explains why Mearsheimer and Rosato’s critique of expected-utility theory is unpersuasive, and how their conception of theory-driven reasoning ignores key aspects of decision-making that national security officials can feasibly address. (...) Lyndon Johnson’s decision to take the United States to war in Vietnam provides a vivid example of how leaders can meet Mearsheimer and Rosato’s criteria for rationality despite clear shortfalls of analytic reasoning. (shrink)

A bi-infinite approximate fixed point of type (n,k) is an approximate fixed point of type (n,k) whose terms are biinfinite; i.e., contain infin-itely many positive and infinitely many negative elements.

We discuss several axiomatizations of set theory in first order predicate calculus with epsilon and a constant symbol W, starting with the simple system K(W) which has a strong equivalence with ZF without Foundation. The other systems correspond to various extensions of ZF by certain large cardinal hypotheses. These axiomatizations are unusually simple and uncluttered, and are highly suggestive of underlying philosophical principles that generate higher set theory.

A number of comparability theorems have been investigated from the viewpoint of reverse mathematics. Among these are various comparability theorems between countable well orderings ([2],[8]), and between closed sets in metric spaces ([3],[5]). Here we investigate the reverse mathematics of a comparability theorem for countable metric spaces, countable linear orderings, and sets of rationals. The previous work on closed sets used a strengthened notion of continuous embedding. The usual weaker notion of continuous embedding is used here. As a byproduct, we (...) sharpen previous results of [3],[5]. (shrink)

On the three most widely discussed contemporary justifications of induction, the inductive justification, the pragmatic justification, and the analytic justification (or dissolution of the problem), none has received widespread acceptance. There are specific problems with each of these approaches and a general problem that affects all three. The purpose of this paper is to provide a fourth justification of induction which is less problematic than or at least problematic in different ways from-the three traditional justifications.

"Moses and Monotheism" is Freud's last book on religion. It was published in its entirety only after his flight from Nazi-occupied Vienna. Moses is perhaps Freud's most controversial book on religion. It is both an apology and a curse. It is a critique of traditional Judaism (by way of an Oedipal analysis of a deified Moses), a defence of a modern humanistic Judaism (a Judaism of moral and intellectual values), and a bitter critique of Christianity (a religion not of the (...) Father but of the sons, a failed religion, which expresses its failure in anti-Semitism). A defiant and rebellious book, one might say, one in which an old man rises to meet his fate and does so with surprising wilfulness and vigour. But Moses also reveals a dogmatic Freud defending a critique of religion that is intellectually flawed and politically misdirected. (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]).