We show that in the Maxwell–Lorentz theory of classical electrodynamics most initial values for fields and particles lead to an ill-defined dynamics, as they exhibit singularities or discontinuities along light-cones. This phenomenon suggests that the Maxwell equations and the Lorentz force law ought rather to be read as a system of delay differential equations, that is, differential equations that relate a function and its derivatives at different times. This mathematical reformulation, however, leads to physical and philosophical consequences for the ontological (...) status of the electromagnetic field. In particular, fields cannot be taken as independent degrees of freedom, which suggests that one should not add them to the ontology. (shrink)

Many arguments have been made against gene editing. This paper addresses the commonly invoked argument that gene editing violates human dignity and is ultimately a subversion of human nature. There are several drawbacks to this argument. Above all, the concept of what human dignity means is unclear. It is not possible to condemn a practice that violates human dignity if we do not know exactly what is being violated. The argument’s entire reasoning is thus undermined. Analyses of the arguments involved (...) in this discussion have often led to the conclusion that gene editing contravenes the principle of genetic identity (genetic immutability) thereby subverting a requisite of human dignity and ultimately threatening human nature. This paper refutes these arguments and shows that any opposition to gene editing cannot rely on the human dignity argument. (shrink)

Ontological expressivism is the view that ontological existence claims express non-cognitive mental states. I develop a version of ontological expressivism that is modeled after Gibbard’s (2003) norm-expressivism. I argue that, when speakers assess whether, say, composite objects exist, they rely on assumptions with regard to what is required for composition to occur. These assumptions guide their assessment, similar to how norms may guide the assessment of normative propositions. Against this backdrop, I argue that “some objects have parts”, uttered in the (...) context of an ontological disagreement, expresses a noncognitive disposition to assess the truth of propositions by using only rules of assessment according to which the proposition that some objects have parts is to be evaluated as true. (shrink)

Theories of graded causation attract growing attention in the philosophical debate on causation. An important field of application is the controversial relationship between causation and moral responsibility. However, it is still unclear how exactly the notion of graded causation should be understood in the context of moral responsibility. One question is whether we should endorse a proportionality principle, according to which the degree of an agent’s moral responsibility is proportionate to their degree of causal contribution. A second question is whether (...) a theory of graded causation should measure closeness to necessity or closeness to sufficiency. In this paper, we argue that we should indeed endorse a proportionality principle and that this principle supports a notion of graded causation relying on closeness to sufficiency rather than closeness to necessity. Furthermore, we argue that this insight helps to provide a plausible analysis of the so-called ‘Moral Difference Puzzle’ recently described by Bernstein. (shrink)

Easy Ontologists, most notably Thomasson (2015), argue that ontological questions are shallow. They think that these questions can either be answered by using our ordinary conceptual competence—of course tables exist!—or are meaningless, or else should be answered through conceptual re-engineering. Ontology thus is “easy”, requiring no distinctively metaphysical investigation. This paper raises a two-stage objection to Easy Ontology. We first argue that questions concerning which entities exist are inextricably bound up with “ontological category questions”, which are questions concerning the identity (...) of and differences between kinds of entities. We then argue that ontological category questions do not have trivial answers, are meaningful, and cannot be answered through conceptual re-engineering. Easy Ontology hence does not constitute a comprehensive ontological methodology. While some of ontology might be easy, category questions form a central part of ontology and are not answered easily. (shrink)

We argue that the epistemic functions of replication in science are best understood by their role in assessing kinds of experimental error. Direct replications serve to assess the reliability of an experiment through its precision: the presence and degree of random error. Conceptual replications serve to assess the validity of an experiment through its accuracy: the presence and degree of systematic errors. To illustrate the aptness of this view, we examine the Hubble constant controversy in astronomy, showing how astronomers have (...) responded to the concordances and discordances in their results by carrying out the different kinds of replication that we identify, with the aim of establishing a precise, accurate value for the Hubble constant. We contrast our view with Machery’s “re-sampling” account of replicability, which maintains that replications only assess reliability. (shrink)

This paper attempts to argue that a radically different notion of freedoms and rights that originates from the other, that is founded on the infinite responsibility for the other, and that demands an encounter with the other as pure alterity, could be a plausible starting point towards the conception and possible realization of a Levinasian society of neighbors. First, an explication is made on why a radical change in the area of freedoms and rights could be the starting point towards (...) a social, political, and moral philosophical framework based on the radical philosophy of Levinas as elaborated in his Otherwise than Being or Beyond Essence. Then, a discussion on conventional conceptions of freedoms and rights, particularly those based on liberalism, libertarianism, and utilitarianism, is presented as groundwork for a comparative analysis between these conventional conceptions and a radical notion that would be entailed by a conception of a Levinasian society of neighbors. Lastly, an attempt is made to characterize a radically different conception of freedoms and rights based on the philosophy of Levinas and to argue how it could be the starting point towards the conception and possible realization of a Levinasian society of neighbors. (shrink)

A central tenet of Heil's ontological conception is a no-levels account of reality, according to which there is just one class of basic properties and relations, while all higher-level entities are configurations of these base-level entities. I argue that if this picture is not to collapse into an eliminativist picture of the world – which, I contend, should be avoided –, Heil's ontological framework has to be supplemented by an independent theory of which configurations of basic entities should count as (...) complex entities. However, such an amendment represents a substantial ontological enhancement, so that the ensuing ontological picture is not as parsimonious as Heil claims it to be. (shrink)

This paper analyzes areas of convergence in the works of Amartya Sen and Slavoj Žižek in their criticisms of the multiculturalist approach to non-violence. First, Žižek’s characterization of the liberal discourse of guilt and fear is presented. Then, Sen’s key ideas on multiculturalism, tolerance, and rational critique are explicated. Next, a synthesis of Sen and Žižek’s notions of universality, freedom, and rationality, as well as of their critical conceptions of globalization and anti-globalization are discussed. Subsequently, Sen and Žižek’s divergences on (...) overcoming violence are examined. Lastly, from integrating Sen and Žižek’s thoughts, key theses are provided on the paradoxical character of the multiculturalist approach to non-violence and on how despite their divergences, both Sen and Žižek propose radical systematic changes and an alternative approach to non-violence characterized by the universals of rationality and genuine freedom. (shrink)

Analyzing causation in terms of Woodward's interventionist theory and describing the structure of the world in terms of causal powers are usually regarded as quite different projects in contemporary philosophy. Interventionists aim to give an account of how causal relations can be empirically discovered and described, without committing themselves to views about what causation really is. Causal powers theorists engage in precisely the latter project, aiming to describe the metaphysical structure of the world. In this paper, I argue that interventionism (...) can benefit from incorporating considerations about causal powers. I describe a previously undiscussed problem for Woodward's definition of an intervention variable that arises when interventionist causal models include disjunctive variables. This problem is solved not by excluding disjunctive (or logically compound) variables per se, but by excluding variables whose values represent disjunctions of too different causal powers. This suggests that interventionism and causal powers theories may be less distant from each other than is often assumed. (shrink)

Defining the distinction between intrinsic and extrinsic properties has turned out to be one of the most difficult and controversial tasks in contemporary metaphysics. It is generally assumed that a definition of intrinsicness should aim to avoid as many counterexamples as possible and reduce the notion to less controversial philosophical notions. In this paper, the author argues for a new methodological approach to defining intrinsicness. Rather than trying to cover as many intuitive examples as possible, a definition of intrinsicness should (...) reflect the crucial features of our intuitive understanding of the notion, and one of these features is that the intrinsic/extrinsic distinction has to be characterized in a non-reductive way. (shrink)

In the remainder of this article, we will disarm an important motivation for epistemic contextualism and interest-relative invariantism. We will accomplish this by presenting a stringent test of whether there is a stakes effect on ordinary knowledge ascription. Having shown that, even on a stringent way of testing, stakes fail to impact ordinary knowledge ascription, we will conclude that we should take another look at classical invariantism. Here is how we will proceed. Section 1 lays out some limitations of previous (...) research on stakes. Section 2 presents our study and concludes that there is little evidence for a substantial stakes effect. Section 3 responds to objections. The conclusion clears the way for classical invariantism. (shrink)

One implication of Vetter's theory of modality is that necessity and possibility are regarded as unitary natural kinds. In this paper, I argue that from the perspective of the philosophy of causation, there are good reasons to distinguish between different kinds of necessity: causal necessity, which is nomologically necessary, and non-causal necessity, which is metaphysically necessary. One challenge for Vetter's approach is to explain this distinction.

Does the Ship of Theseus present a genuine puzzle about persistence due to conflicting intuitions based on “continuity of form” and “continuity of matter” pulling in opposite directions? Philosophers are divided. Some claim that it presents a genuine puzzle but disagree over whether there is a solution. Others claim that there is no puzzle at all since the case has an obvious solution. To assess these proposals, we conducted a cross-cultural study involving nearly 3,000 people across twenty-two countries, speaking eighteen (...) different languages. Our results speak against the proposal that there is no puzzle at all and against the proposal that there is a puzzle but one that has no solution. Our results suggest that there are two criteria—“continuity of form” and “continuity of matter”— that constitute our concept of persistence and these two criteria receive different weightings in settling matters concerning persistence. (shrink)

Globalisation has brought immense changes to the national and international economic structure. The digital revolution and ICT expansion positively impacted the sharing economy development. In this regard, the most avant-garde countries in sharing economy seem to be the advanced countries. However, transitory countries such as Albania are making satisfactory progress as well. While being part of some global cases of sharing economy, Albania is also experiencing domestic incentives related with. The sectors involved in sharing economy are affiliated to different domains, (...) including agriculture, tourism, healthcare, transportation, etc. Albania strongly embraced technology because of its relatively young population and the flexible education system adopting to the market needs. The Albanian government is doing well on the promotion and usage of public platforms, which are supportive of the sharing concept. Although not specifically for the sharing economy, the government of Albania has released some useful strategic plans to embed the necessary instruments and infrastructure to digitalisation. However, there is more to do for sharing economy in specific terms. The collaboration of three actors, businesses-academia-government, would bring to the Albanian market new capacities and additional added values. (shrink)

Formal semantic analyses often take words to be minimal building blocks for the purposes of compositionality. But various recent theories of morphology and syntax have converged on the view that there is no demarcation line corresponding to the word level. The same conclusion has emerged from the compositional semantics of superlatives. In the spirit of extending compositionality below the word level, this paper explores how a small set of particles (Japanese KA and MO, Chinese DOU, and Hungarian VALA/VAGY, MIND, and (...) IS) form quantifier words and serve as connectives, additive and scalar particles, question markers, and existential verbs. The main question is whether the meanings of these particles across the varied environments are highly regular, or they are lexicalized with a variety of different meanings that bear a family resemblance. This paper does not reach definitive conclusions, but it raises analytical possibilities using Boolean semantics and the semantics of alternatives. It also draws attention to systematic similarities and some differences between MO and DOU that have not been studied in the literature. (shrink)

Socioeconomic status refers to the family's social and economic standing in society. It is measured by combining an individual or group's economic and social position, which is often based on income, education, and occupation. It significantly affects academic performance and even one's health status. The pandemic changed the educational system, causing a huge transition from traditional learning methods to online learning. This shift resulted in confusion, burden, and difficulty among students from different walks of life. This study was conducted to (...) determine the academic stress on online learning among nursing students in relation to their economic status and their ability to access technology. The study utilized a quantitative-correlational method aided by a standard questionnaire. Two hundred thirty-six University of Bohol nursing students enrolled in the second semester of SY 2021–2022 were included in the study by random selection. Data revealed a significant correlation between economic status and the level of stress related to academic expectations and a significant correlation between economic status and access to technology after being subjected to the Spearman rho test of correlation. However, no significant correlation was found between access to technology and the respondents' level of academic stress. (shrink)

In this paper, we present an overview of the collaborative economy situation in Portugal. The chapter starts by presenting a number of local platforms and services. Overall, there seems to be a concern about the risk involved in the unregulated development of rental and mobility services. Therefore, we also highlight an overview of laws and regulations concerning the sharing economy platforms, especially for renting. This paper also presents issues related to rental platforms and touristification. We also present a list of (...) the major local shared economy platforms and services. (shrink)

Vera Zasulich’s shooting of Trepov, a governor of St Petersburg who had ordered the flogging of a political prisoner, in January 1878, catapulted her to international fame as a revolutionary heroine, a reputation that she put to good use by becoming one of the five ‘founding parents’ of Russian Marxism that created the ‘Group for the Emancipation of Labour’ in 1883. But her act of self-sacrifice also triggered, to her dismay, the institutionalisation of individual terrorist tactics in the Russian (...) Populist movement with the creation of the ‘People’s Will’ (Narodnaya Volya) Party in 1879. The organisation went into decline after the killing of Tsar Alexander II in 1881, and Populism itself was increasingly superseded by Marxism as the hegemonic force on the left with the rise of the Russian Social Democratic Labour Party (RSDLP). But individual terrorist tactics reappeared with the creation of the Socialist Revolutionary Party in 1902, prompting Zasulich to write an article for Die neue Zeit, the theoretical organ of German Social Democracy, in which she both condemned the Neo-Populist tendency as deleterious to the rising labour movement and supported the organisational plans for the RSDLP sponsored by the Iskra group, developed at length by Lenin in his book What Is to Be Done?, published in March 1902. This article provides the background to Vera Zasulich’s article ‘The Terrorist Tendency in Russia’ (December 1902), setting it against the history of the Russian revolutionary movement from 1878 to 1902. (shrink)

L’indagine condotta su alcuni personaggi finora rimasti nell’ombra, ma che ebbero un peso notevole, se non determinante, sul destino del filosofo, permette di ricostruire il complotto ordito dall’Inquisizione Cattolica per arrivare a mettere le mani su Giordano Bruno. La minuziosa e circostanziata ricostruzione dei fatti si integra perfettamente con altre recenti ricerche dello stesso genere.

As its Latin title says, this article inquires whether there is a single correct list of the moral virtues. Virtue ethics tells us to “act in accordance with the virtues” but can often be accused, for example in Aristotle's Ethics, of helping itself without argument to an account of what the virtues are. This paper is, stylistically, an affectionate tribute to the Angelic Doctor, and it works with a correspondingly Thomistic background and approach. It argues for the view that there (...) is at least one correct list of the virtues, and that we can itemise at least seven items in the list, namely, the four cardinal and the three theological virtues. (shrink)

Nei Pensieri sulla vera valutazione delle forze vive Kant stabilisce il concetto di “mondo” per mezzo di una definizione wolffiana. Nonostante questa recezione, Kant non condivide con Wolff e i wolffiani principi fondanti della cosmologia in quanto sapere metafisico. Il contributo chiarisce come Kant metta in evidenza l'inadeguatezza della definizione wolffiana rispetto a problemi basilari della cosmologia, come la possibilità di dimostrare l'unicità del mondo e l'unità dell'universo. A differenza di precedenti interpretazioni, il contributo sostiene che Kant prova a (...) ovviare a questa inadeguatezza proponendo un riesame del concetto di luogo e una nuova concezione delle relazioni esterne della sostanza. In riferimento a questo tema il contributo offre una nuova interpretazione delle riflessioni di Kant sulla dimensionalità dell'estensione mostrandone la rilevanza per comprendere la sua prima concezione dello spazio. (shrink)

Interview with the professor Maura Pardini Bicudo Véras, former dean and current coordinator of the Postgraduate Program in Social Sciences at the Pontifical Catholic University of São Paulo.

This article proposes, firstly, a general study of the ideological positioning of the Société scientifique de Bruxelles during the first forty years of its existence by means of a detailed reconstruction of its programme, and, secondly, a specific account of its situation within the alternative represented by the Intransigent and Progressive Catholic camps. In order to achieve this objective, it favours the motto of the Société and the figure of its second Secretary, namely Paul Mansion, basing itself primarily on a (...) corpus of texts consisting of his annual reports and those of his predecessor, Father Carbonnelle. While taking particular care in identifying that which, following the Roman injunction in 1890, might have differentiated Mansion’s mandate from Carbonnelle’s, it offers to test the hypothesis that this difference lies, not only in a more favourable attitude towards neo-Thomism, but also in the transition from an intransigent apologetics to a more balanced apologetics. (shrink)

I Gedanken rappresentano il primo momento sintetico della speculazione kantiana. In essi è affrontata la celebre querelle delle forze vive, occasionata da Leibniz nel 1686 nei riguardi della filosofia cartesiana attorno al tema della conservazione della quantità di moto. Già da questo primo scritto emerge chiaramente il filo conduttore che attraversa tutta la ricerca scientifica di Kant, volta al perseguimento di una descrizione sistematica dell’Universo, antecedentemente determinata (a priori), secondo l’indirizzo programmatico della Scienza “classica”, vale a dire in assoluta conformità (...) rispetto alla legge di causalità e al principio di ragion suffi ciente, secondo cui: posita ratione, ponitur rationatum. (shrink)

Alonzo Church famously provided three principal competing criteria for “strict synonymy,” i.e., sameness of semantic content. These are his Alternatives (0), (1), and (2)—numbered in order of increasing course-grainedness of content. On Alternative (2), expressions are deemed strictly synonymous iff they are logically equivalent. This criterion seems hopeless as an account of the objects of propositional attitude. On Alternative (1), expressions are deemed synonymous iff they are λ-convertible. Alternative (1) also evidently conflicts with discourse about the attitudes. On Alternative (...) (0), expressions are deemed strictly synonymous iff they are “synonymously isomorphic” in Church’s sense. On Alternative (0), semantic content is so fine-grained that not even “Romeo loves Juliet” and “Juliet is loved by Romeo” qualify as strictly synonymous. A fourth alternative, here called “Alternative (3),” deems expressions strictly synonymous iff they are co-intensional, i.e., they have the same semantic extension with respect to the same possible worlds. This criterion’s notion of content is even more course grained than that of Alternative (2). Several objections to Alternative (3) are considered. (This article is contained within the author’s more definitive “Singular Concepts”.). (shrink)

This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church's Logic of Sense and Denotation. Church understands such senses themselves to be "sense-functions," functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain undesirable results given certain unusual or "deviant" sense-functions. Certain absurdities result, e.g., an argument can be found for equating any (...) two senses of the same type. An alternative treatment of the senses of functions is discussed, and is thought to do better justice to Frege's original theory. (shrink)

Kyle Stanford has recently given substance to the problem of unconceived alternatives, which challenges the reliability of inference to the best explanation (IBE) in remote domains of nature. Conjoined with the view that IBE is the central inferential tool at our disposal in investigating these domains, the problem of unconceived alternatives leads to scientific anti-realism. We argue that, at least within the biological community, scientists are now and have long been aware of the dangers of IBE. We re-analyze the nineteenth-century (...) study of inheritance and development (Stanford’s case study) and extend it into the twentieth century, focusing in particular on both classical Mendelian genetics and the studies by Avery et al. on the chemical nature of the hereditary substance. Our extended case studies show the preference of the biological community for a different methodological standard: the vera causa ideal, which requires that purported causes be shown on non-explanatory grounds to exist and be competent to produce their effects. On this basis, we defend a prospective realism about the biological sciences. (shrink)

Alonzo Church proposed a theory of sequences of functions and their arguments as surrogates for Russellian singular propositions and singular concepts. Church’s proposed theory accords with his Alternative (0), the strictest of his three competing criteria for strict synonymy. The currently popular objection to strict criteria like (0) on the basis of the Russell-Myhill antinomy is rebutted. Russell-Myhill is not a problem specifically for Alternative (0); it is a refutation of unrestrained concept comprehension. Criteria more lax than (0) are (...) philosophically inadequate. It is shown, however, that Church’s proposed theory is vulnerable under (0) to a version of Russell’s notorious Gray’s Elegy objection. Some amendments to Church’s proposal are proffered, including an amendment, first proposed in the author’s _Frege’s Puzzle_ (1986), that addresses Russell’s objection. Church’s response (personal correspondence) is considered. (shrink)

Corcoran’s 27 entries in the 1999 second edition of Robert Audi’s Cambridge Dictionary of Philosophy [Cambridge: Cambridge UP]. -/- ancestral, axiomatic method, borderline case, categoricity, Church (Alonzo), conditional, convention T, converse (outer and inner), corresponding conditional, degenerate case, domain, De Morgan, ellipsis, laws of thought, limiting case, logical form, logical subject, material adequacy, mathematical analysis, omega, proof by recursion, recursive function theory, scheme, scope, Tarski (Alfred), tautology, universe of discourse. -/- The entire work is available online free at more (...) than one website. Paste the whole URL. http://archive.org/stream/RobertiAudi_The.Cambridge.Dictionary.of.Philosophy/Robert.Audi_The.Cambrid ge.Dictionary.of.Philosophy -/- The 2015 third edition will be available soon. Before you think of buying it read some reviews on Amazon and read reviews of its competition: For example, my review of the 2008 Oxford Companion to Philosophy, History and Philosophy of Logic,29:3,291-292. URL: http://dx.doi.org/10.1080/01445340701300429 -/- Some of the entries have already been found to be flawed. For example, Tarski’s expression ‘materially adequate’ was misinterpreted in at least one article and it was misused in another where ‘materially correct’ should have been used. The discussion provides an opportunity to bring more flaws to light. -/- Acknowledgements: Each of these entries was presented at meetings of The Buffalo Logic Dictionary Project sponsored by The Buffalo Logic Colloquium. The members of the colloquium read drafts before the meetings and were generous with corrections, objections, and suggestions. Usually one 90-minute meeting was devoted to one entry although in some cases, for example, “axiomatic method”, took more than one meeting. Moreover, about half of the entries are rewrites of similarly named entries in the 1995 first edition. Besides the help received from people in Buffalo, help from elsewhere was received by email. We gratefully acknowledge the following: José Miguel Sagüillo, John Zeis, Stewart Shapiro, Davis Plache, Joseph Ernst, Richard Hull, Concha Martinez, Laura Arcila, James Gasser, Barry Smith, Randall Dipert, Stanley Ziewacz, Gerald Rising, Leonard Jacuzzo, George Boger, William Demopolous, David Hitchcock, John Dawson, Daniel Halpern, William Lawvere, John Kearns, Ky Herreid, Nicolas Goodman, William Parry, Charles Lambros, Harvey Friedman, George Weaver, Hughes Leblanc, James Munz, Herbert Bohnert, Robert Tragesser, David Levin, Sriram Nambiar, and others. -/- . (shrink)

As emphasized by Alonzo Church and David Kaplan (Church 1974, Kaplan 1975), the philosophies of language of Frege and Russell incorporate quite different methods of semantic analysis with different basic concepts and different ontologies. Accordingly we distinguish between a Fregean and a Russellian tradition in intensional semantics. The purpose of this paper is to pursue the Russellian alternative and to provide a language of intensional logic with a model-theoretic semantics. We also discuss the so-called Russell-Myhill paradox that threatens simple (...) Russellian type theory if propositions satisfies very strict principles of individuation. One way of avoiding the paradox is to adopt a ramified rather than a simple theory of types. (shrink)

Critique of Alonzo Church's Translation Test. Church's test is based on a common misconception of the grammar of (so-called) quotations. His conclusion (that metalogical truths are actually contingent empirical truths) is a reductio of that conception. Chruch's argument begs the question by assuming that translation must preserve reference despite altering logical form of statements whose truth is explained by their form.

Standard compositionality is the doctrine that the semantic content of a compound expression is a function of the semantic contents of the contentful component expressions. In 1954 Hilary Putnam proposed that standard compositionality be replaced by a stricter version according to which even sentences that are synonymously isomorphic (in the sense of Alonzo Church) are not strictly synonymous unless they have the same logical form. On Putnam’s proposal, the semantic content of a compound expression is a function of: (i) (...) the contentful component expressions; and (ii) the expression’s logical form. Kit Fine recently expanded and modified Putnam’s idea into a sweeping theory in philosophy of language and philosophy of mind. The present paper is a detailed critique of Fine’s “semantic relationism.” Fine’s notion of coordination is explained in terms of the familiar pragmatic phenomenon of recognition. A serious error in Fine’s formal disproof of standard Millianism is exposed. It is demonstrated furthermore that Church’s original criticism of Putnam’s proposal can be extended to Fine’s semantic relationism. Finally, it is also demonstrated that the positive position Fine proffers to supplant standard Millianism is in fact exactly equivalent to standard Millianism, so that Fine’s overall position not only does not displace standard Millianism but is in fact inconsistent. (shrink)

Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands). -/- By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive (...) way of fleshing out this idea is synonymous with a ZF-like theory. -/- This Theorem has rich applications; it realizes John Conway's (1976) Mathematicians' Liberation Movement; and it connects with a lovely idea due to Alonzo Church (1974). (shrink)

“Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is actually a familiar part of our traditional intuitive logical framework (...) and that it is not an artificial formalism created by specialists for technical purposes. To illustrate some of the main relationships between second-order logic and first-order logic, this paper introduces basic logic, a kind of zero-order logic, which is more rudimentary than first-order and which is transcended by first-order in the same way that first-order is transcended by second-order. The heuristic effectiveness and the historical importance of second-order logic are reviewed in the context of the contemporary debate over the legitimacy of second-order logic. Rejection of second-order logic is viewed as radical: an incipient paradigm shift involving radical repudiation of a part of our scientific tradition, a tradition that is defended by classical logicians. But it is also viewed as reactionary: as being analogous to the reactionary repudiation of symbolic logic by supporters of “Aristotelian” traditional logic. But even if “genuine” logic comes to be regarded as excluding second-order reasoning, which seems less likely today than fifty years ago, its effectiveness as a heuristic instrument will remain and its importance for understanding the history of logic and mathematics will not be diminished. Second-order logic may someday be gone, but it will never be forgotten. Technical formalisms have been avoided entirely in an effort to reach a wide audience, but every effort has been made to limit the inevitable sacrifice of rigor. People who do not know second-order logic cannot understand the modern debate over its legitimacy and they are cut-off from the heuristic advantages of second-order logic. And, what may be worse, they are cut-off from an understanding of the history of logic and thus are constrained to have distorted views of the nature of the subject. As Aristotle first said, we do not understand a discipline until we have seen its development. It is a truism that a person's conceptions of what a discipline is and of what it can become are predicated on their conception of what it has been. (shrink)

On a very natural conception of sets, every set has an absolute complement. The ordinary cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining classical logic. Indeed, we can develop a boolean algebra of sets arranged in well-ordered levels. I show this by presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly implement Conway’s games and surreal numbers; and a (...) natural extension of BLT is definitionally equivalent with ZF. (shrink)

This book aims to develop certain aspects of Gottlob Frege’s theory of meaning, especially those relevant to intensional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege. (The approach is contrasted with the less historically-minded Logic of Sense and Denotation of Alonzo Church.) Comparisons of Frege’s theory with those of Russell and (...) others are given. It is in the end shown that developing Frege’s theory in these ways reveals serious problems hitherto largely unnoticed, including those possibly rendering a Fregean intensional logic inconsistent even if his naïve class theory is excluded. (shrink)

In a lengthy review article, C. Anthony Anderson criticizes the approach to property theory developed in Quality and Concept (1982). That approach is first-order, type-free, and broadly Russellian. Anderson favors Alonzo Church’s higher-order, type-theoretic, broadly Fregean approach. His worries concern the way in which the theory of intensional entities is developed. It is shown that the worries can be handled within the approach developed in the book but they remain serious obstacles for the Church approach. The discussion focuses on: (...) (1) the fine-grained/coarse-grained distinction, (2) proper names and definite descriptions, (3) the paradox of analysis and Mates’ puzzle, and (4) the logical, semantical, and intentional paradoxes. (shrink)

Expressions are synonymous if they have the same semantic content. Complex expressions are synonymously isomorphic in Alonzo Church’s sense if one is obtainable from the other by a sequence of alphabetic changes of bound variables or replacements of component expressions by syntactically simple synonyms. Synonymous isomorphism provides a very strict criterion for synonymy of sentences. Several eminent philosophers of language hold that synonymous isomorphism is not strict enough. These philosophers hold that ‘Greeks prefer Greeks’ and ‘Greeks prefer Hellenes’ express (...) different propositions even if they are synonymously isomorphic. They hold that the very recurrence (multiple occurrence) of ‘Greeks’ contributes to the proposition expressed something that indicates the very recurrence in question. Kit Fine argues that this thesis, which he labels semantic relationism calls for a radically new conception of semantics. I have argued that the relevant phenomenon is wholly pragmatic, entirely non-semantic. Here I supplement the case with a new argument. No cognition without recognition—or almost none. With this observation, standard Millianism has sufficient resources to confront Frege’s puzzle and related problems without injecting pragmatic phenomena where they do not belong. (shrink)

W. V. Quine’s criterion of ontological commitment is commonly presented as the slogan: “to be is to be the value of a variable”. More specifically, to be is to be in the domain of values of a bound variable attached to a existential quantifier in the body of a theory. If a sentence of our best available theory quantifies over bachelors, so we conclude that, according to it, there are bachelors. Simplicity and the use of logical apparatus for determining this (...) criterion are responsible for many philosophers to adhere to this standpoint within analytical metaphysics. I will argue that despite this strong influence of the Quinean criterion of ontological commitment in many debates, we find at least three interlinked problems in its original formulation: (1) The criterion depends of a clear definition of theory for the determination of the quantifications counting as entailers of ontological commitments. However, Quine does not present such clear concept of what would be a theory and of how to formalize it. Quine develops this notion under just the metaphor of the knowledge fabric, in which we have a group of sentences, which does not suffice for the required account of ontological commitment. (2) There are distinct possibilities of quantifying over given sentences, which leaves room for different ontological commitments associated with the same statement. In that sense, someone could argue that the Quinean solution would be to endorse just the first order predicate logic. Nonetheless, the Quinean should explain why we ought to be restricted to this logic. (3) The previous problems lead to a possible explosion of the Quinean criterion of ontological commitment, making it trivial, because it permits the quantification over any supposed entities and, hence, that anything can exist. Thus, I will discuss Quine’s criterion of ontological commitment in the light of the abovementioned problems, showing that, unless the Quinean presents a more specific definition of theory beyond just a group of sentences, he leads to an explosion of commitments with different entities. I will conclude that, if you understand ‘theory’ as Alonzo Church’s concept of ‘formalized language’, this knot can be undone. However, Church’s concept is much more akin to Carnap’s linguistic framework than to a notion of knowledge fabric “without borders” as the one proposed by Quine. (shrink)

Propositional attitude sentences, such as (1) Pierre believes that snow is white, have proved to be formidably difficult to account for in a semantic theory. It is generally agreed that the that-clause ‘that snow is white’ purports to refer to the proposition that snow is white, but no agreement has been reached on what this proposition is. Sententialism is a semantic theory which tries to undermine the very enterprise of understanding what proposition is referred to in (1): according to sententialists, (...) in (1) reference is made to the sentence “Snow is white”. Sententialism is generally considered doomed. The two main reasons why are the famous translation argument, firstly suggested by Alonzo Church, and a problem raised by Stephen Schiffer. The purpose of this paper is to provide a unified solution to both criticisms. What I take to be the key ingredient sententialists may exploit is an observation that concerns the nature of languages and quotations: since quotation marks display the quoted material, if you are a speaker of the language the quoted material belongs to, you usually cannot but understand what is quoted. Moreover, I show that sententialists may appeal to that very observation also in order to answer another problem, pointed out by Kent Bach. I conclude that there are good reasons for resisting the temptation of introducing propositions in order to account for propositional attitude sentences. (shrink)

It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church's “lambda calculus” for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903–1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the lambda calculus. Russell also anticipated Schönfinkel's combinatory logic approach of treating multiargument functions as functions having other functions as (...) value. Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and “value-ranges”. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the lambda calculus. (shrink)

Enligt ett realistiskt synsätt kan ett påstående vara sant trots att det inte ens i princip är möjligt att veta att det är sant. En sanningsteoretisk antirealist kan inte godta denna möjlighet utan accepterar en eller annan version av Dummetts vetbarhetsprincip: (K) Om ett påstående är sant, så måste det i princip vara möjligt att veta att det är sant. Det kan dock förefalla rimligt, även för en antirealist, att gå̊ med på̊ att det kan finnas sanningar som ingen faktiskt (...) vet (har vetat, eller kommer att veta) är sanna. Man kan därför tänka sig att en antirealist skulle acceptera principen (K) utan att därför gå med på den till synes starkare principen: (SK) Om ett påstående är sant, så måste det faktiskt finnas någon som vet att det är sant. Ett mycket omdiskuterat argument – som ytterst går tillbaka till Alonzo Church, men som först publicerades i en uppsats av Frederic Fitch i Journal of Symbolic Logic 1963 – tycks emellertid visa att principen (K) implicerar principen (SK). Anta nämligen att (K) är sann, medan (SK) inte är det. Men om (SK) är falsk, så finns det ett påstående som är sant men som ingen faktiskt vet är sant. Anta nu att p är ett sådant påstående. Låt Kp betyda att någon vet att p är sant. Det galler alltså̊ att p är sant samtidigt som Kp inte är det. Betrakta nu påståendet (p ∧ −Kp). Enligt antagandet är detta påstående sant. Enligt (K) måste det då vara möjligt att någon vet att (p ∧ −Kp). D.v.s., det måste vara möjligt att påståendet K(p ∧ −Kp) är sant. Men i så fall är det också̊ möjligt att påståendet Kp ∧ K−Kp är sant, vilket i sin tur implicerar att det är möjligt att Kp ∧ −Kp är sant, vilket ju är absurt. Således kan inte (K) vara sann samtidigt som (SK) är falsk. Vi tycks således kunna sluta oss till att (K) implicerar (SK). I uppsatsen diskuterar jag några olika sätt att undgå̊ Church-Fitch paradoxala slutsats. Ett tillvägagångssätt är att ersätta kunskapsoperatorn med en hierarki av kunskapspredikat. Ett annat är baserat på distinktionen mellan faktisk och potentiell kunskap och ett förkastande av den vanliga modallogiska formaliseringen av principen (K). Den senare typen av lösning betraktas både från ett realistiskt och ett icke-realistiskt perspektiv. Utifrån denna analys kommer jag fram till slutsatsen att vi, vare sig vi är realister eller antirealister rörande sanning, kan sluta oroa oss för vetbarhetsparadoxen och ändå uppskatta Church-Fitchs argument. (shrink)

There is an inconsistency among claims made (or apparently made) in separate articles by Alonzo Church concerning Frege's distinction between sense and denotation taken together with plausible assertions by Frege concerning his notion of ungerade Sinn-i.e., the sense that an expression allegedly takes on in positions in which it has ungerade Bedeutung, denoting its own customary sense. As with any inconsistency, the difficulty can be avoided by relinquishing one of the joint assumptions from which contradiction may be derived. Yet (...) what seems the most plausible resolution, in light of Church's own arguments, involves abandoning the theory of sense and denotation, in the form in which it has been staunchly advocated by both Frege and Church. That theory has come under sustained criticism from several quarters. Whereas the present difficulty supplements the case against the theory, it is unlike more familiar criticisms, since it is not framed from the perspective of an alternative theory (or picture) but is based instead on an internal conflict, and therefore has special force. (shrink)

El objetivo de este artículo es presentar dos tópicos de Lógica matemática y sus fundamentos: El primer tópico es una actualización de la demostración de Alonzo Church del Teorema de completitud de Gödel para la Lógica de primer orden, la cual aparece en su texto "Introduction to Mathematical Logic" (1956) y usa el procedimientos efectivos de Forma normal prenexa y Forma normal de Skolem; y el segundo tópico es una demostración de que la propiedad de partición (tipo Ramsey) del (...) espacio topológico de Baire llamada "Propiedad de partición polarizada" es falsa en el Modelo Básico de Cohen. (shrink)

Forthcoming in Darren Bradley (ed.), Carnap and Contemporary Philosophy. -/- This paper is centered on Carnap’s views on rationality. More specifically, much of the focus is on a puzzle regarding Carnap’s view on rationality that Florian Steinberger has recently discussed. Not only is Steinberger’s discussion of significant intrinsic interest: his discussion also raises general questions about Carnap interpretation. As I have discussed in earlier work, there are two very different ways of interpreting Carnap’s talk of “frameworks” – and, relatedly, different (...) ways of interpreting Carnap’s principle of tolerance. Carnap can be interpreted as either a relativist or as what I call a language pluralist. Steinberger’s puzzle arises given the relativist interpretation; I believe the language pluralist interpretation is correct. Most of the discussion will concern the correct interpretation of Carnap, and what this means for Steinberger’s puzzle. While I will not here mount a full defense of the language pluralist interpretation, I will pause to discuss Vera Flocke’s recent criticism of it. Towards the end, I will describe a puzzle regarding rationality different from Steinberger’s. The puzzle that I describe does arise already for the language pluralist. (shrink)

There can be no doubt that discrimination based on sex, race, ethnicity, religion or beliefs should not be tolerated in academia. Surprisingly, however, in recent years, policies of Diversity, Inclusion and Equity(DIE), officially introduced to counteract discrimination, have increasingly led to quite the opposite result: the exclusion of individuals who do not share a radical 'woke' ideology on identity politics (feminism, other gender activisms, critical race theory, etc.), and to the suppression of the academic freedom to discuss such dogmas. This (...) subversion of academia ― disguised Trojan-horse style as universal human rights advocacy ― is unacceptable because academia must be politically neutral and protect freedom of speech, a cornerstone of professional scholarly activity without which universities as we know them will slowly but surely suffocate. -/- Our purpose here is to put together some particularly illustrative cases of such repression in a single book, testifying to a ubiquitous trend within western culture, irreducible to a few isolated complaints. The essays contained here illustrate the abuse of power, censorship and witch-hunts at many universities and research centres in the name of DIE. -/- List of coauthors in alphabetical order: Dorian Abbot, Tomonori Agoh, Gerhard Amendt, Ivar Arpi, David Benatar, Peter Boghossian, Civitas Research Team, David Díaz Pardo de Vera, Pedro Domingos, Janice Fiamengo, Étienne Forest, Jorge Gibert Galassi, Norman Goldstuck, José L. González Quirós, Lawrence M. Krauss, Patrick LaBelle, Martín López Corredoira, Heather Mac Donald, Martin Malmgren, Erik. J. Olsson, Jordan Peterson, Constantin Polychronakos, Philip C. Salzman, Alessandro Strumia, Tom Todd, Andrei Yafaev. (shrink)