We give an exponential lower bound on the number of proof-lines in intuitionistic propositional logic, IL, axiomatised in the usual Frege-style fashion; i.e., we give an example of IL-tautologies A1,A2,… s.t. every IL-proof of Ai must have a number of proof-lines exponential in terms of the size of Ai. We show that the results do not apply to the system of classical logic and we obtain an exponential speed-up between classical and intuitionistic logic.

The article offers a rigorous explication of the intuitive notion of verisimilitude, I.E., Of the distance of a theory from the truth. The proposal is defended against charges of material inadequacy made by popper, Niniluoto, And miller.

It is well known that the manner in which a definitely descriptive term contributes to the meaning of a sentence depends on the place the term occupies in the sentence. A distinction is accordingly drawn between ordinary contexts and contexts variously termed non-referential, intensional, oblique, or opaque. The aim of the present article is to offer a general account of the phenomenon, based on transparent intensional logic. It turns out that on this approach there is no need to say (as (...) Frege does) that descriptive terms are referentially ambiguous or to deny (as Russell does) that descriptive terms represent self-contained units of meaning. There is also no need to tolerate (as Montague does) exceptions to the Principle of Functionality. The notion of an ordinary (i.e., non-intensional) context is explicated exclusively in terms of logical structure and it is argued that two aspects of ordinariness (termed hospitality and exposure) must be distinguished. (shrink)

The article offers a rigorous truth condition for subjunctively conditional statements. The theory is framed in the system of transparent intensional logic and takes connections (especially the cause-Effect relation) as basic. Counterexamples are given to rival theories based on the notion of world similarity.

Leopoldo Zea was one of the most influential philosophers of the twentieth century. Though in English-language scholarship Zea is known primarily as a historian of ideas, his philosophical producti...

I. The framework. 1, Aristotle's project and methods. 2, The perceptual capacity of the soul. 3, The sensory apparatus. 4, The common sense and the related capacities -- II. The terminology. 1, Overlooked occurrences of the phrase 'common sense'. 2, De anima III.1 425a27. 3, De partibus animalium IV.10 686a31. 4, De memoria et reminiscentia 1 450a10. 5, De anima III.7 431b5. 6, Conclusions on the terminology -- III. Functions of the common sense. 1, Simultaneous perception and cross-modal binding. 2, (...) Perceptual discrimination. 3, Waking, sleep, and control of the senses. 4, Perceiving that what we see and hear, and monitoring of the senses. 5, Other roles of the common sense -- Conclusion. (shrink)

Of two false theories, One can be, Intuitively, Closer to the truth than the other. The purpose of the article is to propose a rigorous explication of this intuitive notion.

Buzaglo (as well as Manders (J Philos LXXXVI(10):553–562, 1989)) shows the way in which it is rational even for a realist to consider ‘development of concepts’, and documents the theory by numerous examples from the area of mathematics. A natural question arises: in which way can the phenomenon of expanding mathematical concepts influence empirical concepts? But at the same time a more general question can be formulated: in which way do the mathematical concepts influence empirical concepts? What I want to (...) show in the present paper can be described as follows. The problem articulated by Buzaglo deserves some semantic refinements. Following explications are needed: What is meaning? (In particular: What are concepts?) What are questions? (Or, equivalently: Semantics of interrogative sentences.) -/- Further, a useful notion will be the notion of problem. Taking over the notion of conceptual system from Materna (Conceptual Systems. Logos, Berlin, 2004) and using Tichý’s Transparent intensional logic (TIL) I can try to solve the problem of the relation between mathematical and empirical concepts (not only for the case of expanding some mathematical concepts). (shrink)

This essay sheds additional light on the biographies and fates of Ayn Rand’s closest relatives in the Soviet Union and abroad after young Alissa Rosenbaum left the “country of workers and peasants” in 1926 for the pursuit of a new life in the United States. Previously unknown facets of her relatives’ lives were intertwined with the complex and often tragic historical events of the first half of the twentieth century. Among these relatives are victims of the German blockade of Leningrad, (...) a music teacher, a European bacteriologist, a doctor who was twice a refugee, and a Soviet Medical Service Corps officer. (shrink)

Chapter One: Constructions. Entities, constructions, and functions When one travels from Los Angeles to New York, going, say, by way of St. Louis, Chicago, ...

Traxler, Pickering, and Clifton found that ambiguous sentences are read faster than their unambiguous counterparts. This so-called ambiguity advantage has presented a major challenge to classical theories of human sentence comprehension because its most prominent explanation, in the form of the unrestricted race model, assumes that parsing is non-deterministic. Recently, Swets, Desmet, Clifton, and Ferreira have challenged the URM. They argue that readers strategically underspecify the representation of ambiguous sentences to save time, unless disambiguation is required by task demands. When (...) disambiguation is required, however, readers assign sentences full structure—and Swets et al. provide experimental evidence to this end. On the basis of their findings, they argue against the URM and in favor of a model of task-dependent sentence comprehension. We show through simulations that the Swets et al. data do not constitute evidence for task-dependent parsing because they can be explained by the URM. However, we provide decisive evidence from a German self-paced reading study consistent with Swets et al.'s general claim about task-dependent parsing. Specifically, we show that under certain conditions, ambiguous sentences can be read more slowly than their unambiguous counterparts, suggesting that the parser may create several parses, when required. Finally, we present the first quantitative model of task-driven disambiguation that subsumes the URM, and we show that it can explain both Swets et al.'s results and our findings. (shrink)

We give an exponential lower bound on number of proof-lines in the proof system K of modal logic, i.e., we give an example of K-tautologies ψ₁, ψ₂,... s.t. every K-proof of ψi must have a number of proof-lines exponential in terms of the size of ψi. The result extends, for the same sequence of K-tautologies, to the systems K4, Gödel—Löb's logic, S and S4. We also determine some speed-up relations between different systems of modal logic on formulas of modal-depth one.

Intensions feature prominently among the entities we talk about.

Modal logic S5 is commonly viewed as an epistemic logic that captures the most basic properties of knowledge. Kripke proved a completeness theorem for the first-order modal logic S5 with respect to a possible worlds semantics. A multiagent version of the propositional S5 as well as a version of the propositional S5 that describes properties of distributed knowledge in multiagent systems has also been previously studied. This article proposes a version of S5-like epistemic logic of distributed knowledge with quantifiers ranging (...) over the set of agents, and proves its soundness and completeness with respect to a Kripke semantics. (shrink)

One of the most prevalent rationales for public healthcare policies is a human right to healthcare. Governments are the typical duty-bearers, but they differ vastly in their capacity to help those vulnerable to serious health problems and those with severe disabilities. A right to healthcare is out of the reach of many developing economies that struggle to provide the most basic services to their citizens. If human rights to provision of such goods exist, then governments would be violating rights without (...) doing anything wrong. I argue that such variable ability to provide healthcare depends not only on financial resources, but on institutional capacity, and that the latter represents a more fundamental challenge to the existence of a human right to healthcare than previously recognized. This challenge does not imply that government has no obligations to protect and improve the health of their citizens, but that it is best to think of such obligations as generated by conventional rights, namely rights arising from local legal and social conventions, which require governments to pursue health-related moral goals such as reducing suffering, closing opportunity gaps for the disadvantaged, and preventing the spread of contagious diseases. We need not think of such moral goals in terms of human rights. (shrink)

In this paper, I would like to present Aristotle’s attitude to sense-perception. I will refer to this attitude as “perceptual optimism”. Perceptual optimism is, very briefly, the position that the senses give us full access to reality as it is. Perceptual optimism entails perceptual realism, the view that there is a reality out there which is accessible to our senses in some way or other, and the belief that our senses are veridical at least to some extent, but it is (...) more comprehensive than that. For instance, a perceptual optimist does not admit such things as qualities which are perceptible in principle but not by us or bodies too small to be perceptible. In this paper I argue that Aristotle is a perceptual optimist, since he believes that reality, at least in the sublunary sphere, is indeed fully accessible to our senses. In the first and largest part of this paper, I will show, in seven distinct theses, what Aristotle’s perceptual optimism entails. In the second and shorter part, I will put Aristotle’s position in a wider context of his epistemology and show why it was important for him to be a perceptual optimist. (shrink)

Despite relative neglect in the literature, Kant’s published and unpublished writings in theoretical philosophy reveal a sustained and at times ambivalent effort to come to terms with the problem of miracles. Because they entail a form of supernatural causation that undermines the law-governedness of the order of nature, miracles pose a significant problem for Kant’s metaphysics. I explore in detail Kant’s account of miracles in conjunction with the relevant aspects of his metaphysics of nature in order to establish in what (...) sense miracles are possible, and how they fit into Kant’s architectonic more generally. (shrink)

Propositional and notional attitudes are construed as relations (-in-intension) between individuals and constructions (rather than propositrions etc,). The apparatus of transparent intensional logic (Tichy) is applied to derive two rules that make it possible to export existential quantifiers without conceiving attitudes as relations to expressions (sententialism).

2 Popper's Logical Definition of Verisimilitude. 3 Popper's Probabilistic Definition of Verisimilitude. 4 Conclusion.

Journal Name: Apeiron Issue: Ahead of print.