For all i ≥ 1, Ti+11 is not ∀Σb2-conservative over Ti1.

The epidemic of human immunodeficiency virus (HIV) and acquired immunodeficiency syndrome (AIDS) has led to many ethical problems. Most studies have focused on the ethical issues faced by nurses who provide care to persons with AIDS (PWA), rather than the ethical issues faced by PWAs themselves. The purpose of this study, therefore, was to explore the ethical issues faced by five HIV/AIDS-infected African-American women. An analysis of interview data revealed that these women deal with four broad categories of ethical issues: (...) diagnosis; disclosure; treatment by, and of, others; and future pregnancies. The results of this study provide an initial description of the ethical issues faced by HIV/AIDS-infected African-American women, and begin to lay the foundation necessary for nurses appropriately to facilitate and support their decisions. (shrink)

Prominent thinkers such as Kripke and Rescher hold that Russell has no modal logic, even that Russell was indisposed toward modal logic. In Part I, I show that Russell had a modal logic which he repeatedly described and that Russell repeatedly endorsed Leibniz's multiplicity of possible worlds. In Part II, I describe Russell's theory as having three ontological levels. In Part III, I describe six Parmenidean theories of being Russell held, including: literal in 1903; (...) universal in 1912; timeless in 1914; transcendental in 1918–1948. The transcendental theory underlies the primary level of Russell's modal logic. In Part IV, I examine Rescher's view that Russell and modal logic did not mix. (shrink)

In this article, I explore the connections between imagination, names, and discoveries by engaging with the works of Alfred North Whitehead and Bertrand Russell. While these two thinkers had divergent philosophical perspectives, I argue that their ideas can be fruitfully integrated into the broader framework of the philosophy of scientific discovery. First, I examine Whitehead’s notion of imagination, distinguishing between two types: counterfactual reasoning within a given theoretical framework and imaginative narrative construction that reshapes the framework itself. This distinction, (...) I suggest, helps clarify how imagination contributes to scientific discoveries. Second, I revisit Russell’s theory of names, proposing a reinterpretation in light of contemporary debates. I advocate for a predicativist reading of Russell’s theory, which, I argue, provides a better account of how names function in the process of scientific discovery—particularly in the naming of newly identified species or concepts. By integrating Whitehead’s insights on imagination and Russell’s refined theory of names, I offer a systematic contribution to the philosophy of scientific discovery, highlighting the structural role of both conceptual tools in shaping scientific progress. (shrink)

The editors of the Handbook of the History of Logic adopted various strategies of narration in particular volumes of the entire work. Presentations are sometimes o...

The analytic movement advertised its 'linguistic turn' as a radical break from the two-thousand-year-old substance tradition. But this is an illusion. On the fundamental level of ontology, there is enough reformulation and presupposition of traditional 'no entity without identity' themes to analogize Frege, Russell, Wittgenstein, and Quine to Aristotle as paradigmatic of modified realism. Thus the pace of ontology is glacial. Frege and Russell, not Wittgenstein and Quine, emerge as the true analytic progenitors of 'no entity without identity,' (...) offering between them at least twenty-nine private language arguments and sixty-four 'no entity without identity' theories. (shrink)

Fregean theories of descriptions as terms have to deal with improper descriptions. To save bivalence various proposals have been made that involve assigning referents to improper descriptions. While bivalence is indeed saved, there is a price to be paid. Instantiations of the same general scheme, viz. the one and only individual that is F and G is G, are not only allowed but even required to have different truth values.

In the years following Bertrand Russell's visit in China, fragments from his work on mathematical logic and the foundations of mathematics started to enter the Chinese intellectual world. While up...

The years 2020 and 2021 mark a centenary since the great British polymath Bertrand Russell visited China. One hundred years after the visit of the preeminent British philosopher Bertrand Russell to...

This paper critically discusses two points concerning some recent views about the concept of truth. Firstly, contrary to Davidson, it shows that meaning of sentences cannot be explicated by T-equivalences. In particular, “is true” is an extensional predicate, but “means that” an intensional one. Secondly, the minimalist account of truth does not provide a satisfactory analysis of the concept of falsity. In this respect, minimalism does not satisfy Russell’s claim that any adequate truth-theory must be a theory of falsity (...) as well. (shrink)

A many-faceted beast, the metaphysics of relations can be approached from many angles. One could begin with the various ways in which relational states are expressed in natural language. If a more historical treatment is wanted, one could begin with Plato, Aristotle, or Leibniz. In the following, I will approach the topic by first drawing on Russell’s Principles of Mathematics (1903) (still a natural-enough starting point), and then turn to a discussion mainly of positionalism. The closing section contains an (...) overview of the six contributions to this Special Issue. (shrink)

This volume brings together selected works by the philosopher Rosemarie Rheinwald (1948–2009). The title "Logic, Causation, Freedom" indicates the broad range of topics, which extends from the Achilles paradox to the problem of free will. Rheinwald preferred to address difficult and fundamental problems: logical and semantic paradoxes, the riddles of inductive reasoning, and the nature of causation. Over the years, her early research interests in the philosophy of mathematics, logic, and the philosophy of science were joined by interests in the (...) philosophy of mind, epistemology, and metaphysics. Each essay in this collection is preceded by an introductory note by a philosopher who knew Rheinwald and is familiar with her work. The introductory notes contain information about the context of the discussion and critical objections, as well as personal memories and comments. An annotated bibliography at the end of the volume provides information about all of Rosemarie Rheinwald's publications, including those that were not included in this collection. May this volume keep alive the memory of a lovely person and encourage further engagement with her impressive work. (shrink)

Bertrand Russell once pointed out that modern science doesn’t deal with causal laws and that assuming otherwise is not only wrong but such thinking is erroneously thought to do no harm. However, looking into the scientific practice of simulation or experimentation reveals a general causal comprehension of physical processes. In this paper I trace causal experiences to the existence of innate causal capacity by which we organize sensory information. This capacity, I argue, is something we have got in virtue (...) of natural selection as can be seen from experiments with intelligent animals like crows and chimpanzees. So understanding the empirical world is impossible without the use of causal categories. The reason why Russell believed that modern science does not refer to causal laws is, I think, because he argued that the laws of mathematical physics give us a non-causal description of reality. In contrast to such a claim I hold that theoretical laws are prescriptive rules of description rather than descriptions themselves. (shrink)

In the literature, regress arguments often take one of two different forms: either they conclude that a given solution fails to solve any problem of a certain kind (the strong conclusion), or they conclude that a given solution fails to solve all problems of a certain kind (the weaker conclusion). This gives rise to a logical problem: do regresses entail the strong or the weaker conclusion, or none? In this paper I demonstrate that regress arguments can in fact take both (...) forms, and clearly set out the logical difference between them. Throughout the paper, I confine myself to metaphysical examples from the early Russell. Only now that we know they are valid can we start to discuss whether they are sound. (shrink)

The focus of the article is the self-predication principle, according to which the/a such-and-such is such-and-such. We consider contemporary approaches (Frege, Russell, Meinong) to the self-predication principle, as well as fourteenth-century approaches (Burley, Ockham, Buridan). In crucial ways, the Ockham-Buridan view prefigures Russell’s view, and Burley’s view shows a striking resemblance to Meinong’s view. In short the Russell-Ockham-Buridan view holds: no existence, no truth. The Burley-Meinong view holds, in short: intelligibility suffices for truth. Both views approach self-predication (...) in a uniform way. We were unable to find a medieval philosopher who, like Frege, approaches self-predication in a non-uniform way. We do not want to dispute that there are also considerable differences between the contemporary and the fourteenth-century approach to self-predication. Importantly, fourteenth-century accounts of self-predication rely strongly on the identity theory of predication, and this theory is not endorsed by contemporary philosophers of language. Nevertheless, some basic tenets seem to us to be clearly shared between fourteenth-century and contemporary thinkers. (shrink)

In this paper it is shown that addition of certain reductions to the standard cut removing reductions of deductions in prepositional logic makes prepositional logic non-normalizable. From this follows that some provable propositions in prepositional logic has no direct proof.

What is logical relevance? Anderson and Belnap say that the “modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance.” But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson–Belnap manner. Thus modern classical logicians such as Peirce, Frege, Russell, (...) Wittgenstein, and Quine are implicit relevantists on the deepest level. In showing this, I reunite two fields of logic which, strangely from the traditional point of view, have become basically separated from each other: relevance logic and diagram logic. I argue that there are two main concepts of relevance, intensional and extensional. The first is that of the relevantists, who overlook the presence of the second in modern classical logic. The second is the concept of truth-ground containment as following from in Wittgenstein’s Tractatus. I show that this second concept belongs to the diagram tradition of showing that the premisses contain the conclusion by the fact that the conclusion is diagrammed in the very act of diagramming the premisses. I argue that the extensional concept is primary, with at least five usable modern classical filters or constraints and indefinitely many secondary intensional filters or constraints. For the extensional concept is the genus of deductive relevance, and the filters define species. Also following the Tractatus, deductive relevance, or full truth-ground containment, is the limit of inductive relevance, or partial truth-ground containment. Purely extensional inductive or partial relevance has its filters or species too. Thus extensional relevance is more properly a universal concept of relevance or summum genus with modern classical deductive logic, relevantist deductive logic, and inductive logic as its three main domains. (shrink)

Bertrand Russel asked in a newspaper column (1932) of astrologers: “Do they believe themselves in the sciences that they profess?” This paper asks whether academic psychologists believed the science that they professed. The replication crisis—researchers do not obtain results comparable to the original when repeating that study—has, in the past decade, seriously challenged psychology's status as a science. Most of the social and behavioral sciences have been invalidated by the replication crisis, but I focus on psychology because of my personal (...) involvement in this field. I draw on the work of Žižek and Zupančič on denial and disavowal to approach the question of what we believed. I will argue, contra Zupančič, that disavowal is not necessarily a phenomenon of mass individualism. As doctoral students, we learned to transgress scientific norms, and then to act as if this transgression had never happened. To enter the community of scientists, we had to disavow that psychology is not a science. After running enough studies—falling on our knees and praying—some of us came to believe that psychology is a science, whilst others held on to a more cynical position. Subjectively some of us believed, some did not, objectively we all believed. I also pursue the related questions of why we did what we did—why was it, for psychology as a field, necessary to break scientific norms and what enjoyment did we, as subjects, derive from what we were doing? (shrink)

Mathematical logic was first introduced to China in early 1920s. Although, the process of introduction was facilitated by the lectures of Bertrand Russel at Peking University in 1921 and continued by China’s most passionate adherents of Russell’s philosophy, the establishment of mathematical logic as an academic discipline occurred only in late 1920s, in the framework of a recently reorganised Qinghua University in Peking. The main aim of this paper is to shed some light on the process of establishment of (...) mathematical logic at the department of philosophy at Qinghua University, between the years 1926 and 1945. In its main line of discussion, the article highlights the curricular developments at the department, connecting them with concrete theoretical endeavours by the leading members of the department. Furthermore, in its later parts, the article summarises the main advances made in the context of studies of modern logic at Qinghua University, from the expositions on the quintessential work Principia Mathematica, to the subsequent integration of criticisms coming from circles of logicians at Harvard University and ground-breaking contributions of Kurt Gödel in the mid-1930s. (shrink)

This paper examines how the work of Frege was known and received in Poland in the period 1910–1935 (with one exception concerning the later work of Suszko). The main thesis is that Frege's reception in Poland was perhaps faster and deeper than in other countries, except England, due to works of Russell and Jourdain. The works of Łukasiewicz, Leśniewski and Czeżowski are described.

Ray Monk and Anthony Palmer (eds.), Bertrand Russell and the Origins of Analytical Philosophy. Introduction by Ray Monk and Anthony Palmer. Bristol, U.K.:Thoemmes Press, 1996. xvi + 383 pp. £48.00/$78.00 (cloth); £16.95/$29.95 (paper).

Les Premiers Analytiques sont pour Lukasiewicz un livre de logique et non de philosophie. Il dit meme que cet ouvrage de pure logique ne contient aucune contamination philosophique. Mais cela ne veut pas dire qu'il n'a rien a apprendre aux philosophes et aux metaphysiciens sur les formalismes et sur les modalites. Comme le dit Lukasiewicz: Il reste encore des philosophes en activite auxquels il ne serait peut-etre pas impossible de suggerer qu'ils devraient acquerir une bonne connaissance de la logique dite (...) mathematique avant de traiter de la logique et de son histoire; ils eviteraient ainsi de perdre leur temps, leurs lecteurs de meme, ce qui n'est peut-etre pas denue d'importance pratique. Lukasiewicz est l'un des philosophes de l'Ecole de Lvov-Varsovie, courant philosophique majeur du XXe siecle. Son premier livre portait sur le principe de contradiction chez Aristote. Il en montrait l'importance, mais aussi la fragilite logique. Son dernier livre, consacre a la syllogistique, une partie de la logique, porte de nouveau sur Aristote. Pour peu qu'elle n'ignore pas Frege, les matrices logiques de Peirce, les Principia Mathematica de Russell et Whitehead ainsi que les apports considerables des logiciens polonais, comme Lesniewski, Sfupecki, et Lukasiewicz lui-meme, l'histoire de la logique, et en l'occurrence l'etude des Premiers Analytiques, constitue une voie d'acces privilegiee pour comprendre ce que sont les formalismes. (shrink)

Arnošt Kolman (1892–1979) was a Czech mathematician, philosopher and Communist official. In this paper, we would like to look at Kolman’s arguments against logical positivism which revolve around the notion of the fetishization of mathematics. Kolman derives his notion of fetishism from Marx’s conception of commodity fetishism. Kolman is aiming to show the fact that an entity (system, structure, logical construction) acquires besides its real existence another formal existence. Fetishism means the fantastic detachment of the physical characteristics of real things (...) or phenomena from these things. We identify Kolman’s two main arguments against logical positivism. In the first argument, Kolman applied Lenin’s arguments against Mach’s empiricism-criticism onto Russell’s neutral monism, i.e. mathematical fetishism is internally related to political conservativism. Kolman’s second main argument is that logical and mathematical fetishes are epistemologically deprived of any historical and dynamic dimension. In the final parts of our paper we place Kolman’s thinking into the context of his time, and furthermore we identify some tenets of mathematical fetishism appearing in Alain Badiou’s mathematical ontology today. (shrink)

The paper focuses on the inferential role of quantifiers in Frege, Peano and Russell. Two aspects of the early years of mathematical logic are discussed: the gradual perfection of the principles of reasoning with quantifiers, and the presumed conceptual impossibility of posing metatheoretical questions, as embodied in Jean van Heijenoort’s well-known dictum about “logic as calculus and logic as language.”.

For animal research, the precautionary principle was written into public policy through the so-called three R’s of replacement, reduction, and refinement. These guidelines, as developed by Russell and Burch six decades ago, aimed to establish safeguards against the abuse of animals in the pursuit of science. While these safeguards, which started from the basic premise that science itself would benefit from a reduction of animal suffering, seem compelling at first, the three R’s have in practice generated a degree of (...) confusion while opening up loopholes that have enabled researchers to effectively dismiss some of the more inconvenient aspects of ethical concerns. Such problems have been discussed in detail by multiple authors. Here, we suggest a different approach by arguing that a clear parallel can be drawn between the shortcomings evident in the current three R’s model and the flawed practice of early modern judicial torture, in which a set of elaborate safeguards that were designed to prevent abuses served instead to create the same combination of confusion and easily exploited loopholes. In the case of judicial torture, attempts to refine the system from within produced limited results, and effective change only took place when individual legal systems succeeded in enforcing clear absolutes. We explore the implications of this for the regulation of animal research by pointing to the need for achievable absolutes, based on a clear, evidence-based, and publicly deliberated rationale, in order to facilitate and improve research ethics. (shrink)

In preparation for his article on Russell’s mathematical logic (1944), Gödel read carefully Peano’s Arithmetices Principia. His six pages of summary in the Gabelsberger shorthand contain a remarkable analysis of the formal structure of Peano’s proofs which is diametrically opposed to the common view that Peano’s treatise contained no formal deductive machinery.

Existuje překvapivě málo knih, které by se pokoušely o syntetizující pohled na analytickou filosofii. Je ovšem pravda, že ve druhé polovině našeho století se soubor filosofů, kteří se k analytické filosofii hlásí nebo kteří k ní bývají řazeni, stává natolik různorodý, že se jakákoli syntéza stává problematickou; překvapivě málo syntetizujících prací existuje ale i o ‘klasické’ analytické filosofii, to jest o analytické filosofii období zhruba od konce devatenáctého století do poloviny století dvacátého. Dejnožkova kniha je jednou z těch mála, které (...) se o něco takového pokouší, a to je třeba přivítat. Dejnožka se ovšem nesnaží podat všestranný rozbor názorů klasiků analytické filosofie; soustředí se pouze jeden aspekt jejich učení, totiž na jejich ontologii. Hned v úvodu své knihy k tomu vysvětluje, jaké opodstatnění může mít hovořit o ontologii u takového druhu filosofie, která se programově distancuje od metafyziky. Podle něj je tomu tak, že i když se někteří analytičtí filosofové někdy více či méně úspěšně vyhýbali otázkám metafyzickým (to jest otázkám po nejzákladnějších kategoriích bytí), ontologickým otázkám (to jest otázkám po povaze bytí jako takového) se v podstatě vyhnout nelze. A Dejnožka se snaží ukázat, že klasikové analytické filosofie se těmito otázkami zabývali mnohdy velice do hloubky. To je patrné zejména u Frega a Russella, kterým autor věnuje největší pozornost; avšak k těm, kteří podle Dejnožky berou ústřední otázku ontologie za svou, řadí Dejnožka i Wittgensteina i Quina (jimž se však věnuje na pouze velice omezeném prostoru - každému asi na dvanácti stránkách). (shrink)

Although Russell’s theory of definite descriptions is highlyappreciated in the area of philosophy of language, it has faced some objections from different angles. One of the major objections is known as the objection arising from incomplete definite descriptions. According to this objection, a speaker by his/her utterance of a sentence containing an incomplete definite description often succeeds in saying something true despite the fact that such a sentence always expresses a false proposition. This particular objection against Russell’s theory (...) arises because of an ignorance concerning the distinction between the meaning of a sentence and the assertion made by a speaker by using that sentence in a particular context. To address this distinction between meaning and assertion Scott Soames’ theory concerning the connection between meaning and assertion has been adopted. With the help of this theory, it has been shown that the problem arising from incomplete definite descriptions does not pose a genuine threat to Russell’s theory. Philosophy and Progress, Vol#73-74; No#1-2; Jan-Dec 2023 P 317-336. (shrink)

This is a critical review of a book that defends two basic theses about analytic philosophy--that the 'no entity without identity' ontology is basic to the four great analytic philosophers and that they were 'modified realists.' This review calls into question both of these claims. The ontological views of Frege, Russell, Quine, Wittgenstein and others are discussed as well other central issues in analytic philosophy.