Ketamine, a dissociative anesthetic commonly used by US physicians, has recently been shown to be a powerful anti-depressant and is also capable of eliciting transpersonal experiences that can be transformative. Although currently approved in the US only for use as an anesthetic, physicians there can legally prescribe it off-label to treat various psychological/ psychiatric problems and it has been used for these non-anesthetic purposes in Argentina, Iran, Mexico, Russia, and the UK, as well as in the US. The literature on (...) using ketamine psychotherapeutically is reviewed and two case studies using ketamine-enhanced psychotherapy for treating death anxiety in terminally-ill people are reported. The potential importance of beginning formal research on using KEP during end-of-life for those suffering death anxiety is emphasized. (shrink)

The ability to engage in and recognize pretend play begins around 18 months. A major challenge for theories of pretense is explaining how children are able to engage in pretense, and how they are able to recognize pretense in others. According to one major account, the metarepresentational theory, young children possess both production and recognition abilities because they possess the mental state concept, PRETEND. According to a more recent rival account, the Behavioral theory, young children are behaviorists about pretense, and (...) only produce and recognize pretense as a sort of behavior--namely, behaving 'as-if'. We review both the metarepresentational and Behavioral accounts and argue that the Behavioral theory fails to characterize very young children's abilities to produce and to recognize pretense. Among other problems, the Behavioral theory implies that children should frequently mis-recognize regular behavior as pretense, while certain regular forms of pretend play should neither be produced nor recognized. Like other mental states, pretense eludes purely behavioral description. The metarepresentational theory does not suffer these problems and provides a better account of children's pretense. 2016 APA, all rights reserved). (shrink)

Recently, Rueger and Sharp (1996) and Koperski (1998) have been concerned to show that certain procedural accounts of model confirmation are compromised by non-linear dynamics. We suggest that the issues raised are better approached by considering whether chaotic data analysis methods allow for reliable inference from data. We provide a framework and an example of this approach.

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.

Young children’s failures in reasoning about beliefs and desires, and especially about false beliefs, have been much studied. However, there are few accounts of successful belief-desire reasoning in older children or adults. An exception to this is a model in which belief attribution is treated as a process wherein an inhibitory system selects the most likely content for the belief to be attributed from amongst several competing contents [Leslie, A. M., & Polizzi, P. (1998). Developmental Science, 1, 247–254]. We tested (...) this model with an ‘avoidance false belief task’ in which subjects predict the behavior of a character, who wants to avoid an object but who is mistaken about which of three locations it is in. The task has two equally correct answers—in seeking to avoid the location where she mistakenly believes the object to be, the character might equally go to the location where the object actually is, or to the remaining empty location. However, the model predicts that subjects will prefer one of these answers, selecting the object’s actual location over the empty location. This bias was confirmed in a series of five experiments with children aged between 4 and 8 years of age. A sixth experiment ruled out two rival explanations for children’s biased responding. Two further experiments found the opposite bias in adults. These findings support one selection model as an account of belief-desire reasoning in children, and suggest that a different model is needed for adults. The process of selecting contents for mental state attributions shows a developmental shift between 8 years of age and adulthood. (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).

Two countable well orderings are weakly comparable if there is an order preserving injection of one into the other. We say the well orderings are strongly comparable if the injection is an isomorphism between one ordering and an initial segment of the other. In [5], Friedman announced that the statement “any two countable well orderings are strongly comparable” is equivalent to ATR 0 . Simpson provides a detailed proof of this result in Chapter 5 of [13]. More recently, (...) class='Hi'>Friedman has proved that the statement “any two countable well orderings are weakly comparable” is equivalent to ATR 0 . The main goal of this paper is to give a detailed exposition of this result. (shrink)

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.

Erich Fromm was a political activist, psychologist, psychoanalyst, philosopher, and one of the most important intellectuals of the twentieth century. Known for his theories of personality and political insight, Fromm dissected the sadomasochistic appeal of brutal dictators while also eloquently championing love--which, he insisted, was nothing if it did not involve joyful contact with others and humanity at large. Admired all over the world, Fromm continues to inspire with his message of universal brotherhood and quest for lasting peace. The first (...) systematic study of Fromm's influences and achievements, this biography revisits the thinker's most important works, especially _Escape from Freedom_ and _The Art of Loving_, which conveyed important and complex ideas to millions of readers. The volume recounts Fromm's political activism as a founder and major funder of Amnesty International, the National Committee for a Sane Nuclear Policy, and other peace groups. Consulting rare archival materials across the globe, Lawrence J. Friedman reveals Fromm's support for anti-Stalinist democratic movements in Central and Eastern Europe and his efforts to revitalize American democracy. For the first time, readers learn about Fromm's direct contact with high officials in the American government on matters of war and peace while accessing a deeper understanding of his conceptual differences with Freud, his rapport with Neo-Freudians like Karen Horney and Harry Stack Sullivan, and his association with innovative artists, public intellectuals, and world leaders. Friedman elucidates Fromm's key intellectual contributions, especially his innovative concept of "social character," in which social institutions and practices shape the inner psyche, and he clarifies Fromm's conception of love as an acquired skill. Taking full stock of the thinker's historical and global accomplishments, Friedman portrays a man of immense authenticity and spirituality who made life in the twentieth century more humane than it might have been. (shrink)

This is the initial publication on Concept Calculus, which establishes mutual interpretability between formal systems based on informal commonsense concepts and formal systems for mathematics through abstract set theory. Here we work with axioms for "better than" and "much better than", and the Zermelo and Zermelo Frankel axioms for set theory.

Let k ≥ 2 and f:Nk Æ [1,k] and n ≥ 1 be such that there is no x1 < ... < xk+1 £ n such that f(x1,...,xk) = f(x1,...,xk+1). Then we want to find g:Nk+1 Æ [1,3] such that there is no x1 < ... < xk+2 £ n such that g(x1,...,xk+1) = g(x2,...,xk+2). This reducees adjacent Ramsey in k dimensions with k colors to adjacent Ramsey in k+1 dimensions with 3 colors.

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.

The considerable attention to financial interests in clinical research has focused mostly on academic medical centers, even though the majority of clinical research is conducted in community practice settings. To fill this gap, this article maps the practices and policies in 73 community hospitals and several hundred specialized facilities around the country for reviewing clinical investigators’ financial relationships with research sponsors. Community hospitals face a substantially different mix of issues than academic medical centers do because their physician researchers are usually (...) not employees, and more of their studies are later-phase, multicenter trials. Accordingly, community physicians stand to benefit personally from per capita payments, but they tend to have less direct influence over research findings when compared with their academic peers. These and other contrasts require separate guidance for community-based organizations that takes into account their particular needs, circumstances, and institutional capacities. (shrink)

We show the algorithmic unsolvability of a number of decision procedures in ordinary two dimensional Euclidean geometry, involving lines and integer points. We also consider formulations involving integral domains of characteristic 0, and ordered rings. The main tool is the solution to Hilbert's Tenth Problem. The limited number of facts used from recursion theory are isolated at the beginning.

I don’t remember if I got as high as 2-390, but I distinctly remember taking my first logic course - as a Freshman - with Hartley Rogers, in Fall 1964 - here in 2-190. Or was it in 2-290?

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.

Since then we have been engaged in the development of such results of greater relevance to mathematical practice. In January, 1997 we presented some new results of this kind involving what we call “jump free” classes of finite functions. This Jump Free Theorem is treated in section 2.

We have been particularly interested in the demonstrable unremovability of machinery, which is a theme that can be pursued systematically starting at the most elementary level - the use of binary notation to represent integers; the use of rational numbers to solve linear equations; the use of real and complex numbers to solve polynomial equations; and the use of transcendental functions to solve differential equations.

Let R Õ [1,n]3k ¥ [1,n]k. We define R = {y Œ [1,n]k:($xŒA3)(R(x,y))}. We say that R is strictly dominating if and only if for all x,yŒ[1,n]k, if R(x,y) then max(x) < max(y).

It turns out, time and time again, in order to make serious progress in f.o.m., we need to take actual reasoning and actual development into account at precisely the proper level. If we take these into account too much, then we are faced with information that is just too difficult to create an exact science around - at least at a given state of development of f.o.m. And if we take these into account too little, our findings will not have (...) the relevance to mathematical practice that could be achieved. (shrink)

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.

Russell’s way out of his paradox via the impredicative 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.

This topic has been discussed earlier on the FOM email list in various guises. The common theme is: big numbers and long sequences associated with mathematical objects. See..

The equation P = NP concerns algorithms for deciding membership in sets. The consensus is that P ≠ NP, although some prominent experts guess otherwise.

NOTE: This is an expanded version of my lecture at the special session on reverse mathematics, delivered at the Special Session on Reverse Mathematics held at the Atlanta AMS meeting, on January 6, 2005.

Mathematical Logic had a glorious period in the 1930s, which was briefly rekindled in the 1960s. Any Shock Value, such as it is, has surrounded unprovability from ZFC.

Normal mathematical culture is overwhelmingly concerned with finite structures, finitely generated structures, discrete structures (countably infinite), continuous and piecewise continuous functions between complete separable metric spaces, with lesser consideration of pointwise limits of sequences of such functions, and Borel measurable functions between complete separable metric spaces.

We say that R is strictly dominating if and only if for all x,yŒ[1,n], if R(x,y) then max(x) 3k ¥ [1,n], there exists A Õ [1,n] such that R = A. Furthermore, A Õ [1,n] is unique.

We present some new set and class theoretic independence results from ZFC and NBGC that are particularly simple and close to the primitives of membership and equality. They are shown to be equivalent to familiar small large cardinal hypotheses. We modify these independendent statements in order to give an example of a sentence in set theory with 5 quantifiers which is independent of ZFC. It is known that all 3 quantifier sentences are decided in a weak fragment of ZF without (...) power set. (shrink)

Extrapolating from the work of Mahlo , one can prove that given any pair of countable closed totally bounded subsets of complete separable metric spaces, one subset can be homeomorphically embedded in the other. This sort of topological comparability is reminiscent of the statements concerning comparability of well orderings which Friedman has shown to be equivalent to ATR0 over the weak base system RCA0. The main result of this paper states that topological comparability is also equivalent to ATR0. In (...) Section 1, the pertinent subsystems of second-order arithmetic and results on well orderings are reviewed. Sections 2 and 3 overview the encoding of metric spaces and homeomorphisms in second-order arithmetic. Section 4 contains a proof of the topological comparability result in ATR0. Section 5 contains the reversal, a derivation of ATR0 from the topological comparability result. In Section 6, additional information about the structure of the embeddings is obtained, culminating in an application to closed subsets of the real numbers. (shrink)

i. Proofless text is based on a variant of ZFC with free logic. Here variables always denote, but not all terms denote. If a term denotes, then all subterms must denote. The sets are all in the usual extensional cumulative hierarchy of sets. There are no urelements.

This paper was referred to in the Introduction in our paper [Fr97a], “The Axiomatization of Set Theory by Separation, Reducibility, and Comprehension.” In [Fr97a], all systems considered used the axiom of Extensionality. This is appropriate in a set theoretic context.

We consider intuitionistic number theory with recursive infinitary rules . Any primitive recursive binary relation for which transfinite induction schema is provable is in fact well founded. Its ordinal is less than ε 0 if the transfinite induction schema is intuitionistically provable in elementary number theory. These results are provable intuitionistically. In fact, it suffices to consider transfinite induction with respect to one particular number-theoretic property.