Gentzen's account of logical consequence is extended so as to become a matter of degree. We characterize and study two kinds of function G, where G(X,Y) takes values between 0 and 1, which represent the degree to which the set X of statements (understood conjunctively) logically implies the set Y of statements (understood disjunctively). It is then shown that these functions are essentially the same as the absolute and the relative probability functions described by Carnap.

In his 1936 paper,On the Concept of Logical Consequence, Tarski introduced the celebrated definition oflogical consequence: “The sentenceσfollows logicallyfrom the sentences of the class Γ if and only if every model of the class Γ is also a model of the sentenceσ.” [55, p. 417] This definition, Tarski said, is based on two very basic intuitions, “essential for the proper concept of consequence” [55, p. 415] and reflecting common linguistic usage: “Consider any class Γ of sentences and a sentence which (...) follows from the sentences of this class. From an intuitive standpoint it can never happen that both the class Γ consists only of true sentences and the sentenceσis false. Moreover, … we are concerned here with the concept of logical, i.e.,formal, consequence.” [55, p. 414] Tarski believed his definition of logical consequence captured the intuitive notion: “It seems to me that everyone who understands the content of the above definition must admit that it agrees quite well with common usage. … In particular, it can be proved, on the basis of this definition, that every consequence of true sentences must be true.” [55, p. 417] The formality of Tarskian consequences can also be proven. Tarski's definition of logical consequence had a key role in the development of the model-theoretic semantics of modern logic and has stayed at its center ever since. (shrink)

The Ramsey-sentence H* of any hypothesis H is shown to be a synthetic proposition containing mathematics as a finite component. Far from being quasi-tautological, H* proves to have as much physical content as H itself.

SummaryExtremism in the environment‐versus innateness controversy in the behavioural sciences and in human sociobiology is being examined. Genetic effects can be severely modified or overruled by environmental factors, but may, nevertheless, be important. Dawkins' view that we are survival machines programmed to subserve selfish genes seems untenable and is a root of racialism. It is also argued that morality is compatible with mixed genetic and environmental control of brains via existing biological machinery.

This paper presents a theoretical elaboration of the ethical framework of classical capitalism as formulated by Adam Smith in reaction to the dominant mercantilism of his day. It is seen that Smith's project was profoundly ethical and designed to emancipate the consumer from a producer and state dominated economy. Over time, however, the various dysfunctions of a capitalist economy — e.g., concentration of wealth, market power — became manifest and the utilitarian ethical basis of the system eroded. Contemporary capitalism, dominated (...) as it is by large corporations, entrenched political interests and persistent social pathologies, bears little resemblance to the system which Smith envisioned would serve the common man. Most critiques of capitalism are launched from a Marxian-based perspective. We find, however, that by illustrating the wide gap between the reality of contemporary capitalism and the model of amoral political economy developed by Smith, the father of capitalism proves to be the most trenchant critic of the current order. (shrink)

Following Henkin’s discovery of partially-ordered (branching) quantification (POQ) with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or “cardinality” quantifiers, e.g., “most”, “few”, “finitely many”, “exactly α ”, where α is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, Henkin definition first to a (...) general definition of monotone-increasing (M↑) POQ and then to a general definition of generalized POQ, regardless of monotonicity. The extension is based on (i) Barwise’s 1979 analysis of the basic case of M↑ POQ and (ii) my 1990 analysis of the basic case of generalized POQ. POQ is a non-compositional 1st-order structure, hence the problem of extending the definition of the basic case to a general definition is not trivial. The paper concludes with a sample of applications to natural and mathematical languages. (shrink)

Suppose COVID-19 is the runaway tram in the famous moral thought experiment, known as the “Bystander at the Switch.” Consider the two differentiated responses of governments around the world to this new threat, namely the option of quarantine/lockdown and herd immunity. Can we contrast the hypothetical with the real scenario? What do the institutional decisions and strategies for dealing with the virus, in the beginning of 2020, signify in a normative moral framework? This paper investigates these possibilities in order to (...) highlight the similarities and, more importantly, the differences that exist between utilitarianism and Kantian ethics. Analysis shows that the hypothetical scenario can never be fully compared to the complex multifactorial nature of the real world. But if a comparison is attempted, the most obvious difference between the two governmental strategies is the concept of duty within the Kantian perspective. Ultimately, it is a matter of comparing freedom and life. Attributing a moral “priority ticket” to one or the other can be analysed through interpersonal aggregation. (shrink)

Central to many issues surrounding reduction in science is the relation between a physical system and its components. In this article we examine how thermodynamic theory relates properties of whole systems to properties of their components. In order to keep the analysis general, we focus our study on universal properties like volume, heat capacity, energy and temperature. In the cases examined we find that scientific explanation requires appeal to properties of components that are spatially as extensive as the whole system. (...) We discuss some implications of our study for the purported paradigmatic reductions of heat and temperature to molecular motion. We conclude that while macro systems reduce ontologically to micro components, epistemologically the reduction of theoretical concepts in general fails. (shrink)

When Aristotle limits the manifestation of true courage to the military context only, his primary target is an overly inclusive conception of courage presented by Plato in the Laches. At the same time, Aristotle explicitly tries to demarcate his ideal of genuine courage from the paradigmatic examples of courageous actions derived from the Homeric epics. It remains questionable, though, whether Aristotle is truly earnest in his efforts to distance himself from Homer. It will be argued that Aristotle's attempt to associate (...) with Homer the two forms of specious courage—courage of the citizen troops and spirit-caused courage—fails to provide sufficient criteria for the demarcation in question. All the essential elements of the Aristotelian account of courage, such as a voluntary choice, a noble goal, and a thumos-driven reaction guided by reason are exemplified by a number of Homeric characters as well. It is thus likely that the philosopher's account of courage largely incorporates the poetic tradition at a new level, rather than supersedes it. (shrink)

A picture held us captive. And we could not get outside it, for it lay in our language and language seemed to repeat it to us inexorably. Wittgenstein.