Worlds and Models in Bayart and Carnap

In the early days of the semantics for modal logic the `possible worlds' were thought of as models or interpretations. This was particularly so when the interpretation was of \emph{logical} necessity or possibility, where this was understood in terms of validity. Arnould Bayart in 1958 may have been the first modal logician to argue explicitly against the identification of necessity and validity. This note contrasts his semantics with that provided by Rudolf Carnap in 1946, and examines Bayart's proof that if you identify necessity with validity then certain theorems of S5 are not valid. The proof is then examined using Carnap's semantics

Revisiting McKinsey's 'Syntactical' Construction of Modality

In 1945 J.C.C. McKinsey produced a ‘semantics’ for modal logic based on necessity defined in terms of validity. The present papers looks at how to update F.R. Drake’s completeness proof for McKinsey’s semantics by comparing McKinsey ‘models’ with the now standard Kripke models. It also looks at the motivation behind the system McKinsey called S4.1, but which we now call S4M; and use this motivation to produce a McKinsey semantics for that system. One lesson which emerges from this work is an appreciation of the superiority of the current possible worlds semantics based on frames and models, both in terms of an intuitive understanding of modality, and also in terms of the ease of working with particular systems

The Completeness of Carnap's Predicate Logic

The paper first proves the completeness of the (non-modal) first-order predicate logic presented in Carnap’s 1946 article ‘Modalities and quantification’. By contrast the modal logic defined by the semantics Carnap produces is unaxiomatisable. One can though adapt Carnap’s semantics so that a standard completeness proof for a Carnapian version of predicate S5 turns out to be available./

Revisiting McKinsey's 'Syntactical' Construction of Modality

In 1945 J.C.C. McKinsey produced a ‘semantics’ for modal logic based on necessity defined in terms of validity. The present papers looks at how to update F.R. Drake’s completeness proof for McKinsey’s semantics by comparing McKinsey ‘models’ with the now standard Kripke models. It also looks at the motivation behind the system McKinsey called S4.1, but which we now call S4M; and use this motivation to produce a McKinsey semantics for that system. One lesson which emerges from this work is an appreciation of the superiority of the current possible worlds semantics based on frames and models, both in terms of an intuitive understanding of modality, and also in terms of the ease of working with particular systems

Worlds and Models in Bayart and Carnap

In the early days of the semantics for modal logic the `possible worlds' were thought of as models or interpretations. This was particularly so when the interpretation was of \emph{logical} necessity or possibility, where this was understood in terms of validity. Arnould Bayart in 1958 may have been the first modal logician to argue explicitly against the identification of necessity and validity. This note contrasts his semantics with that provided by Rudolf Carnap in 1946, and examines Bayart's proof that if you identify necessity with validity then certain theorems of S5 are not valid. The proof is then examined using Carnap's semantics

The Completeness of Carnap's Predicate Logic

The paper first proves the completeness of the (non-modal) first-order predicate logic presented in Carnap’s 1946 article ‘Modalities and quantification’. By contrast the modal logic defined by the semantics Carnap produces is unaxiomatisable. One can though adapt Carnap’s semantics so that a standard completeness proof for a Carnapian version of predicate S5 turns out to be available./

Identification of LIMK2 as a therapeutic target in castration resistant prostate cancer

This study identified LIMK2 kinase as a disease-specific target in castration resistant prostate cancer (CRPC) pathogenesis, which is upregulated in response to androgen deprivation therapy, the current standard of treatment for prostate cancer. Surgical castration increases LIMK2 expression in mouse prostates due to increased hypoxia. Similarly, human clinical specimens showed highest LIMK2 levels in CRPC tissues compared to other stages, while minimal LIMK2 was observed in normal prostates. Most notably, inducible knockdown of LIMK2 fully reverses CRPC tumorigenesis in castrated mice, underscoring its potential as a clinical target for CRPC. We also identified TWIST1 as a direct substrate of LIMK2, which uncovered the molecular mechanism of LIMK2-induced malignancy. TWIST1 is strongly associated with CRPC initiation, progression and poor prognosis. LIMK2 increases TWIST1 mRNA levels upon hypoxia; and stabilizes TWIST1 by direct phosphorylation. TWIST1 also stabilizes LIMK2 by inhibiting its ubiquitylation. Phosphorylation-dead TWIST1 acts as dominant negative and fully prevents EMT and tumor formation in vivo, thereby highlighting the significance of LIMK2-TWIST1 signaling axis in CRPC. As LIMK2 null mice are viable, targeting LIMK2 should have minimal collateral toxicity, thereby improving the overall survival of CRPC patients

Slim Epistemology with a Thick Skin

The distinction between ‘thick’ and ‘thin’ value concepts, and its importance to ethical theory, has been an active topic in recent meta-ethics. This paper defends three claims regarding the parallel issue about thick and thin epistemic concepts. (1) Analogy with ethics offers no straightforward way to establish a good, clear distinction between thick and thin epistemic concepts. (2) Assuming there is such a distinction, there are no semantic grounds for assigning thick epistemic concepts priority over the thin. (3) Nor does the structure of substantive epistemological theory establish that thick epistemic concepts enjoy systematic theoretical priority over the thin. In sum, a good case has yet to be made for any radical theoretical turn to thicker epistemology