We characterize the completely determined Borel subsets of HYP as exactly the [Formula: see text] subsets of HYP. As a result, HYP believes there is a Borel well-ordering of the reals, that the Borel Dual Ramsey Theorem fails, and that every Borel d-regular bipartite graph has a Borel perfect matching, among other examples. Therefore, the Borel Dual Ramsey Theorem and several theorems of descriptive combinatorics are not theories of hyperarithmetic analysis. In the case of the Borel Dual Ramsey Theorem, this (...) answers a question of Astor, Dzhafarov, Montalbán, Solomon and the third author. (shrink)

We improve on and generalize a 1960 result of Maltsev. For a field F, we denote by $H(F)$ the Heisenberg group with entries in F. Maltsev showed that there is a copy of F defined in $H(F)$, using existential formulas with an arbitrary non-commuting pair of elements as parameters. We show that F is interpreted in $H(F)$ using computable $\Sigma _1$ formulas with no parameters. We give two proofs. The first is an existence proof, relying on a result of Harrison-Trainor, (...) Melnikov, R. Miller, and Montalbán. This proof allows the possibility that the elements of F are represented by tuples in $H(F)$ of no fixed arity. The second proof is direct, giving explicit finitary existential formulas that define the interpretation, with elements of F represented by triples in $H(F)$. Looking at what was used to arrive at this parameter-free interpretation of F in $H(F)$, we give general conditions sufficient to eliminate parameters from interpretations. (shrink)

Current work in language models (LMs) helps us speed up or even skip thinking by accelerating and automating cognitive work. But can LMs help us with critical thinking -- thinking in deeper, more reflective ways which challenge assumptions, clarify ideas, and engineer new concepts? We treat philosophy as a case study in critical thinking, and interview 21 professional philosophers about how they engage in critical thinking and on their experiences with LMs. We find that philosophers do not find LMs to (...) be useful because they lack a sense of selfhood (memory, beliefs, consistency) and initiative (curiosity, proactivity). We propose the selfhood-initiative model for critical thinking tools to characterize this gap. Using the model, we formulate three roles LMs could play as critical thinking tools: the Interlocutor, the Monitor, and the Respondent. We hope that our work inspires LM researchers to further develop LMs as critical thinking tools and philosophers and other 'critical thinkers' to imagine intellectually substantive uses of LMs. (shrink)

A number of philosophers maintain that the destruction of an embryo in the first 2 weeks after fertilization is not morally problematic as it is metaphysically impossible for any human organism to then have existed. We contend that the typical adult human organism was once a zygote so there is no metaphysical shortcut to justify early abortion. We show that five arguments against human organisms ever having been zygotes fail. All of the arguments have to do with one variant or (...) another of the zygote or early embryo dividing. They do not provide any reason to believe that since some adult organisms are not identical to zygotes due to earlier divisions, none could have been. (shrink)

In this commentary, I would like to do three things: First, reflect on Voronka’s engagement with the critique of experience as a foundational concept and her answers to this; second, comment on how we, as both activists and user/survivor researchers, engage with other critical discourses emerging from excluded groups; and finally, offer some of my own perspectives and history as a user/survivor researcher and activist in the United Kingdom to illustrate the first two points.I agree with much of what Voronka (...) has to say about the risks of relying on ‘experience’ as an unquestioned category and how those risks are embodied today in the increasing reliance on terms such as ‘experts by experience’ and ‘people... (shrink)

The environment has often been thought to consist of resources that are unowned, and hence subject to the well-known tragedy of the commons. But in recent years, property ideas have been increasingly recruited for environmental protection, in a manner that appears to vindicate the view that property rights evolve along with the needs for resource management. Nevertheless, property regimes have some pitfalls for environmental resources: the relevant parties may not be able to come to agreement; property regimes may be weak (...) or ineffective; they may be aimed at purposes inconsistent with environmental protection; property rights definitions may not work well for environmental resources; modern property regimes may promote monoculture rather than diverse environments. This essay describes these problems and asks to what degree they apply to a new effort to use property rights approaches, namely cap-and-trade programs to control greenhouse gases. It concludes that property rights, while imperfect and something of a retreat from a regime of complete liberty, may offer gains for environmental protection. But success will depend on close attention to the accountability and effectiveness of the governmental institutions necessary to support environmental property regimes. (shrink)