The place of human values in the language of science: Kuhn,Saussure, and structuralism

The current paradigm in medicine generally distinguishes between genetic and environmental causes of disease. Although the word paradigm has become a commonplace, the theories of Thomas Kuhn have not received much attention in the journals of medicine. Kuhn's structuralist method differs radically from the daily activities of the scientific method itself. Using linguistic theory, this essay offers a structuralist reading of Thomas Kuhn's The Structure of Scientific Revolutions. Our purpose is to highlight the similarities between these structuralist models of science and language. In part, we focus on the logic that enables Kuhn to assert the priority of perception over interpretation in the history of science. To illustrate some of these issues, we refer to the distinction between environmental and genetic causes of disease. While the activity of scientific research results in the revision of concepts in science, the production of significant differences that shape our knowledge is in part a social and linguistic process.     

A Note on Graded Modal Logic

We introduce a notion of bisimulation for graded modal logic. Using this notion, the model theory of graded modal logic can be developed in a uniform manner. We illustrate this by establishing the finite model property and proving invariance and definability results.     

基本医疗卫生改革的政治伦理、市场逻辑与未来走向

基本医疗卫生改革是当前实现“2030健康中国”和新时代下践行人民健康优先战略的一项制度创新。然而,现实中改革仍面临医疗资源配置不均和医疗服务供给效率不高的双重困境。本质上,医疗服务具有公利性与私利性二元属性,进而延伸出立足于公利性属性,基本医疗卫生改革应当坚守“人人公平享有”的政治伦理,鉴于私利性属性改革需要维护医疗市场主体合法逐利的正当权利,政府公利性创造与市场私利驱动是辩证性的哲学思考。我国医改未来应以公民健康与福祉共享为价值依归,始终坚持政府严守底线、市场有序竞争、社会和谐稳定的发展主线。     

On the Consistency of the Δ1 1-CA Fragment of Frege's Grundgesetze

It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing ¹ ₁-comprehension schema would already be inconsistent. In the present paper, we show that this is not the case.     

Classical Non-Associative Lambek Calculus

We introduce non-associative linear logic, which may be seen as the classical version of the non-associative Lambek calculus. We define its sequent calculus, its theory of proof-nets, for which we give a correctness criterion and a sequentialization theorem, and we show proof search in it is polynomial.     

A Tale of Four Grammars

In this paper we consider the relations existing between four deductive systems that have been called categorial grammars and have relevant connections with linguistic investigations: the syntactic calculus, bilinear logic, compact bilinear logic and Curry's semantic calculus.     

Entailment with Near Surety of Scaled Assertions of High Conditional Probability

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal is achieved by taking Adams" (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams" logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of ¬ C given B are both close to one but the bound on the former"s deviation from 1 is much smaller than the latter"s, then it may be concluded that in all likelihood the conditional probability of C given A B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor"s rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl"s System-Z ⁺. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their random-structures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL.