The central idea of Lakatos’ quasi-empiricism view of the philosophy of mathematics is that truth values are transmitted bottom-up, but only falsity can be transmitted from basic statements. As it is falsity but not truth that flows bottom-up, Lakatos emphasizes that observation and induction play no role in both conjecturing and proving phases in mathematics. In this paper, I argue that Lakatos’ view that one cannot obtain primitive conjectures by induction contradicts the history of mathematics, and therefore undermines (...) his quasi-empiricism theory. I argue that his misconception of induction causes this view of Lakatos. Finally, I propose that Wittgenstein’s view that “mathematics does have a grammatical nature, but it is also rooted in empirical regularities” suggests the possibility to improve Lakatos’ view by maintaining his quasi-empiricism while accepting the role induction plays in the conjecturing phase. (shrink)

Imre Lakatos' views on the philosophy of mathematics are important and they have often been underappreciated. The most obvious lacuna in this respect is the lack of detailed discussion and analysis of his 1976a paper and its implications for the methodology of mathematics, particularly its implications with respect to argumentation and the matter of how truths are established in mathematics. The most important themes that run through his work on the philosophy of mathematics and which culminate in the 1976a paper (...) are (1) the (quasi-)empirical character of mathematics and (2) the rejection of axiomatic deductivism as the basis of mathematical knowledge. In this paper Lakatos' later views on the quasi-empirical nature of mathematical theories and methodology are examined and specific attention is paid to what this view implies about the nature of mathematical argumentation and its relation to the empirical sciences. (shrink)

A first step is taken towards articulating a constructive empiricist philosophy of mathematics, thus extending van Fraassen's account to this domain. In order to do so, I adapt Field's nominalization program, making it compatible with an empiricist stance. Two changes are introduced: (a) Instead of taking conservativeness as the norm of mathematics, the empiricist countenances the weaker notion of quasi-truth (as formulated by da Costa and French), from which the formal properties of conservativeness are derived; (b) Instead of quantifying (...) over spacetime regions, the empiricist only admits quantification over occupied regions, since this is enough for his or her needs. (shrink)

In this paper, I explore Rosen’s ‘transcendental’ objection to constructive empiricism—the argument that in order to be a constructive empiricist, one must be ontologically committed to just the sort of abstract, mathematical objects constructive empiricism seems committed to denying. In particular, I assess Bueno’s ‘partial structures’ response to Rosen, and argue that such a strategy cannot succeed, on the grounds that it cannot provide an adequate metalogic for our scientific discourse. I conclude by arguing that this result provides (...) some interesting consequences in general for anti-realist programmes in the philosophy of science.Keywords: Constructive empiricism; Mathematical fictionalism; Partial structures; Modality. (shrink)

This paper clarifies and discusses Imre Lakatos’ claim that mathematics is quasi-empirical in one of his less-discussed papers A Renaissance of Empiricism in the Recent Philosophy of Mathematics. I argue that Lakatos’ motivation for classifying mathematics as a quasi-empirical theory is epistemological; what can be called the quasi-empirical epistemology of mathematics is not correct; analysing where the quasi-empirical epistemology of mathematics goes wrong will bring to light reasons to endorse a pluralist view of mathematics.

The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T1, ..., Tn in which Ti+1, for 1 ≤ i < n, supersedes Ti. This thesis has a great philosophical significance because it implies that there is a sense in which mathematical theories, (...) like the theories belonging to the empirical sciences, are fallible and that, consequently, mathematical knowledge has a quasi-empirical nature. The way I have chosen to provide evidence in favour of the correctness of the main thesis of this article consists in arguing that Cantor–Zermelo set theory is a Lakatosian Mathematical Research Programme (MRP). (shrink)

I begin chapter I by discussing two key distinctions that constitute the core of van Fraassen's constructive empiricism: a distinction between observables and unobservables and a distinction between acceptance and belief with regard to a theory. To support constructive empiricism, van Fraassen also deploys two epistemological principles: only actual observations are to be taken as evidence and possible evidence is all that can be rationally inferred from the actual evidence. I reject both principle and van Fraassen's construal of (...) observation. As does van Fraassen, I make the distinction between acceptance and belief in chapter II. I contend that one does not need to be an antirealist to espouse this distinction between acceptance and belief. ;In the remaining chapters, I develop a quasi-Bayesian account of acceptance as an alternative to van Fraassen's. In chapter III, I consider three views of acceptance: van Fraassen's, Bayesian views, and the epistemic view. I argue that both van Fraassen's account and the epistemic account are open to Bayesian objections. However, Bayesianism assumes a controversial principle called "maximization of expected utility" , which might mitigate the impact of the Bayesian objections. ;In the final chapter, I consider different decision principles, e.g. Kyburg's decision principle, and Gardenfors and Sahlin's decision principle. I formulate a decision principle called the "weak-dominance-decision principle " based on Kyburg's theory . The interval-based probability yields, as a limiting case, the point-valued probability when we have complete information about the event in question. In this case, my decision principle reduces to MEU. Therefore, the same Bayesian objections against both van Fraassen's theory of acceptance and the epistemic theory of acceptance could be made from the perspective of my decision principle while escaping the perils of strict Bayesianism. My theory of acceptance is quasi-Bayesian, because WDP rests on interval-based probability. (shrink)

This paper will address the nineteenth-century reception of Bacon as an exponent of materialism in Joseph de Maistre and Karl Marx. I will argue that Bacon’s philosophy is “quasi-materialist.” The materialist components of his philosophy were noticed by de Maistre and Marx, who, in addition, pointed out a Baconian materialist heritage. Their construction of Bacon’s figure as the leader of a materialist lineage ascribed to his philosophy a revolutionary import that was contrary to Bacon’s actual leanings. This contrast shows (...) how different the contexts were within which materialism was conceived and valued across the centuries, and how far philosophical and scientific discourses may be transformed by their receptions, to the point that in many cases they could hardly be embraced by the authors of these discourses. (shrink)

An examination of Carnap's Aufbau in the context of Schlick's Allgemeine Erkenntnislehre of ten years earlier, suggests that Carnap's focus there on the sign-relation (Zeichenbeziehung) is an effort to retrieve a verificationist account of the meaning of individual scientific statements from the abyss of meaning-holism entailed by Schlick's proposal that scientific concepts be implicitly defined. The Aufbau's antipodal aspects, its reductive phenomenalism and quasi-Kantian concern with the constitution of objectivity, are seen as complementary moments of the marriage of (...) class='Hi'>empiricism and a new emphasis on scientific concepts as "free creations of the human mind". (shrink)

According to quasi-empiricism, mathematics is very like a branch of natural science. But if mathematics is like a branch of science, and science studies real objects, then mathematics should study real objects. Thus a quasi-empirical account of mathematics must answer the old epistemological question: How is knowledge of abstract objects possible? This paper attempts to show how it is possible.The second section examines the problem as it was posed by Benacerraf in Mathematical Truth and the next section (...) presents a way of looking at abstract objects that purports to demythologize them. In particular, it shows how we can have empirical knowledge of various abstract objects and even how we might causally interact with them. (shrink)

RESUMENAnalizamos la problemática actual en torno a la demostración matemática, con particular énfasis en las ideas introducidas por las demostraciones asistidas por ordenador y por la llamada matemática experimental. Examinamos además la influencia que pueden tener estas ideas sobre el concepto de demostración y proponemos una caracterización atendiendo a las diferentes funciones que puede desempeñar la demostración en su vertientes explicativa, comunicativa, sistematizadora, como incrementadora de la comprensión de resultados y como transmisora de conocimiento y convicción. Finalmente, se ofrecen algunas (...) conclusiones sobre problemas relacionados con la intuición, la lógica, la certeza, el conocimiento y el falibilismo, desde la perspectiva de las demostraciones, que favorecen una concepción cuasi-empirista de la matemática.PALABRAS CLAVEDEMOSTRACIÓN, DEMOSTRACIÓN ASISTIDA POR ORDENADOR, CONOCIMIENTO MATEMÁTICO, CUASI-EMPIRISMOABSTRACTThe present problems about mathematical proof are analyzed, putting the emphasis on the ideas introduced by the computer-assisted proofs and by the so-called experimental mathematics. In addition, the influence that those may have on the concept of proof is examined, and a characterization is proposed taking into consideration the functions that such a concept of proof may perform according to its different aspects as explanation, communication, systematization, as a way to increase undestading of results, and as a way to transmit knowledge and conviction. Finally, and from this perspective on proofs, some conclusions are offered about problems connected with intuition, logic, certinty, knowledge and falibilism, that favor a quasi-empirical view on mathematics.KEYWORDSPROOF, COMPUTER,-ASSITED PROOF, MATHEMATICAL KNOWLEDGE, QUASI-EMPIRICISM. (shrink)

RESUMENPresentamos la contribución de Th. Tymoczko a la filosofía de la matemática y analizamos y evaluamos las demostraciones asistidas por ordenador y los razonamientos no rigurosos en la matemática experimental, con particular referencia al Teorema de los Cuatro Colores.PALABRAS CLAVETYMOCZKO – CUASI-EMPIRISMO – MATEMÁTICA EXPERIMENTAL – RAZONAMIENTO NO RIGUROSO – DEMOSTRACIONES ASISTIDAS POR ORDENADORABSTRACTWe present Th. Tymoczko’s contribution to the philosophy of mathematics, and we analyze and evaluate the computer-assisted proofs and the non-rigorous reasonings in the experimental mathematics, particularly in (...) reference to the Four-Colour Theorem.KEYWORDTYMOCZKO – QUASI-EMPIRICISM – EXPERIMENTAL MATHEMATICS – NON-RIGOROUS REASONING – COMPUTER-ASSISTED PROOF. (shrink)

RESUMENPresentamos la contribución de Th. Tymoczko a la filosofía de la matemática y analizamos y evaluamos las demostraciones asistidas por ordenador y los razonamientos no rigurosos en la matemática experimental, con particular referencia al Teorema de los Cuatro Colores.PALABRAS CLAVETYMOCZKO – CUASI-EMPIRISMO – MATEMÁTICA EXPERIMENTAL – RAZONAMIENTO NO RIGUROSO – DEMOSTRACIONES ASISTIDAS POR ORDENADORABSTRACTWe present Th. Tymoczko’s contribution to the philosophy of mathematics, and we analyze and evaluate the computer-assisted proofs and the non-rigorous reasonings in the experimental mathematics, particularly in (...) reference to the Four-Colour Theorem.KEYWORDTYMOCZKO – QUASI-EMPIRICISM – EXPERIMENTAL MATHEMATICS – NON-RIGOROUS REASONING – COMPUTER-ASSISTED PROOF. (shrink)

This article explores the comparison between Derrida and Zhuangzi and their approaches to the question of metaphor and analogy, examining the deconstruction of essentialist and culturalist forms of philosophical comparativism. The author contends that the notion of ‘Western metaphysics’ relies on an implicit comparison between the West and its others, shaped not only by philosophical factors but also by historical, sociological and strategic considerations, as exemplified in Aristotle’s exclusion and subjection of metaphor. Derrida’s approach in ‘White Mythology’, with its ‘internal (...) reading’ and ‘quasi-transcendental’ perspective, challenges the unity and identity of the conventional representation of philosophy as a Western achievement. However, the article also advocates for an ‘external’ and ‘quasi-empiricist’ viewpoint that recognises the erratic character of comparisons, resisting the appropriation of philosophical differences into general categories such as ‘Western’ or ‘Chinese philosophy’. (shrink)

This paper calls into question the growing tendency of quasi-absolutism within postmodern mainstream media discourse under the guise of objectivity. The tendency’s major aim is to ascribe more believability to its discourse by re-presenting that which it covers as the vehicle of objective truth to the mainstream audience. Two interweaving discourses have marked such objectivity: one in the form of indoctrinating and omnipresent narratives, which via effective propaganda become tantamount to ritualism, the other epitomised in the nostalgia for rationalisation, (...) already inherent in western positivist thought through the exponential increase of quasi-empiricism. Accordingly, what the media cover exists. What they do not remains in the order of myth. The article starts by rethinking objectivity within modern western academia, a discourse whose objectivity is already flawed from within. Then, with respect to human experience and media coverage, the paper concludes by raising the question of postmodern mainstream media’s substitution of religious quasi-absolutist narratives, be they secular or non-secular. Subjectivity thus emerges as the ultimate ground upon which our being may be legitimate. (shrink)

Mathematics used to be portrayed as a deductive science. Stemming from Polya, however, is a philosophical movement which broadens the concept of mathematical reasoning to include inductive or quasi-empirical methods. Interest in inductive methods is a welcome turn from foundationalism toward a philosophy grounded in mathematical practice. Regrettably, though, the conception of mathematical reasoning embraced by quasi-empiricists is still too narrow to include the sort of thought-experiment which Mueller describes as traditional mathematical proof and which Lakatos examines in (...) Proofs and refutations. This paper extends the concept of mathematical reasoning along two further dimensions to accommodate thought-experiment.Keywords: Thought-experiment; Informal proof; Mathematical reasoning. (shrink)

The article deals with philosophy of mathematics called quasi-empiricism, with special attention paid to concepts of changes in mathematics as a result of social activity during its development. Three outlooks on historical changes in the development of mathematics are presented: Wilder's description of mathematical practise in a cultural framework, Garbiner's analysis of „scientific revolution” in mathematics in the end of 18th century and Kitcher's criticism of invariability and cummulativity of mathematical knowledge and his application of Kuhn's philosophy of (...) science to mathematics. (shrink)

This is the second part of the study concerning the problem of ontological reductions in mathematics. In this part, some major strategies of argumentation in favor of mathematical realism are presented. The versions to be considered are: Gödel’s realism, Quine’s quasi-empiricism and Balaguer’s Full-Blooded Platonism. Some introductory remarks considering the problem of ontological reductions in the context of these three stances are also presented.

This is the third part of the study concerning the problem of ontological reductions in mathematics. In this part, the problem of reconstruction of (parts of) mathematics in theories weaker than full ZFC is discussed. The tools from reverse mathematics are used, and the results are discussed from the point of view of various versions of realism (Gödel’s realism, Quine’s quasi-empiricism and Balaguer’s Full-Blooded Platonism). Some problems concerning the possibility of discussing these problem outside the conceptual system of (...) set theory are also addressed. (shrink)

It is argued that the truth status of emergent properties of complex adaptive systems models should be based on an epistemology of proof by constructive verification and therefore on the ontological axioms of a non-realist logical system such as constructivism or intuitionism. ‘Emergent’ properties of complex adaptive systems models create particular epistemological and ontological challenges. These challenges bear directly on current debates in the philosophy of mathematics and in theoretical computer science. CAS research, with its emphasis on computer simulation, is (...) heavily reliant on models which explore the entailments of Formal Axiomatic Systems. The incompleteness results of G¨odel, the incomputability results of Turing, and the Algorithmic Information Theory results of Chaitin, undermine a realist truth model of emergent properties. These same findings support the hegemony of epistemology over ontology and point to alternative truth models such as intuitionism, constructivism and quasi-empiricism. (shrink)

In this article the problem of unification of mathematical theories is discussed. We argue, that specific problems arise here, which are quite different than the problems in the case of empirical sciences. In particular, the notion of unification depends on the philosophical standpoint. We give an analysis of the notion of unification from the point of view of formalism, Gödel's platonism and Quine's realism. In particular we show, that the concept of “having the same object of study” should be made (...) precise in the case of mathematical theories. In the appendix we give a working proposal of a certain understanding of this notion. (shrink)

This article explores some open questions related to the problem of verification of theories in the context of empirical sciences by contrasting three epistemological frameworks. Each of these epistemological frameworks is based on a corresponding central metaphor, namely: (a) Neo-empiricism and the gambling metaphor; (b) Popperian falsificationism and the scientific tribunal metaphor; (c) Cognitive constructivism and the object as eigen-solution metaphor. Each of one of these epistemological frameworks has also historically co-evolved with a certain statistical theory and method for (...) testing scientific hypotheses, respectively: (a) Decision theoretic Bayesian statistics and Bayes factors; (b) Frequentist statistics and p-values; (c) Constructive Bayesian statistics and e-values. This article examines with special care the Zero Probability Paradox (ZPP), related to the verification of sharp or precise hypotheses. Finally, this article makes some remarks on Lakatos’ view of mathematics as a quasi-empirical science. (shrink)

This paper outlines the intellectual biography of Walter Dubislav. Besides being a leading member of the Berlin Group headed by Hans Reichenbach, Dubislav played a defining role as well in the Society for Empirical/Scientific Philosophy in Berlin. A student of David Hilbert, Dubislav applied the method of axiomatic to produce original work in logic and formalist philosophy of mathematics. He also introduced the elements of a formalist philosophy of science and addressed more general problems concerning the substantiation of human knowledge. (...) What set Dubislav apart from the other logical empiricists was his expertise in the history of logic and exact philosophy which enabled him to elucidate and advance the thinking in both disciplines. In the realm of logic proper, Dubislav is best known for his pioneering work in theory of definitions. What is more, he did original work on the so called ‘quasi truth-tables’ which aided Reichenbach in developing his logic of probability. Dubislav also elaborated an influe.. (shrink)

"Quasi-memories," necessarily presupposing a distinction between an "experiencing" and a "remembering" person, are considered by Parfit and Shoemaker as necessary and/or sufficient criteria for personal identity. However, the concept of "q-memories" is rejected by Schechtman since, according to her, neither "content" and "experience" can be separated from each other in "q-memories" ("principal inseparability") nor can they be distinguished from delusions/confabulations ("principal indistinguishability"). The purpose of the present paper is to demonstrate that, relying on a neurophilosophical approach, both arguments can (...) be rejected. Neuropsychological research shows that "contents" of memories are classified according to the accompanying psychological state such that the same "content" can be classified either as auto- or heterobiographical by the respective "experience." Since "content" and "experience" can be separated from each other, the argument of "principal inseparability" must be rejected on empirical grounds. In addition, as demonstrated in an example of a schizophrenic patient, "q-memories" can be distinguished from delusions/confabulations considering the ability to distinguish between different sources of autobiographical memories as a differential criterion. In conclusion, both arguments by Schechtman against the concept of "q-memories" have to be rejected on the basis of neurophilosophical considerations. Consequently, the concept of "q-memories" can be considered as compatible with current empirical knowledge. (shrink)

This chapter identifies three main sources of the Stoic elements in Hobbes's philosophy: the early Christian‐Stoic Tertullian, the modern “Neo‐Stoic” school of Justus Lipsius, and the natural philosophers of the Cavendish Circle he frequented. Perhaps the most direct Stoical impact on Hobbes was the second/third century Church Father Tertullian. Hobbes and Cavendish are at bottom kindred Stoic spirits, though their systems diverge on the precise nature of material activity. The chapter explores the Stoic character of Hobbesian space, time, causality, and (...) God, especially as these notions are employed in his natural philosophy. Hobbes's quasi‐realism about imaginary space is highly reminiscent of the Stoics' conception of pure space as one of the problematic “incorporeals.” The chapter shows that Hobbes's metaphysical views, though quite unorthodox in his day, served to buttress his overall materialist, empiricist, and mechanist program in natural philosophy. (shrink)

I show that the partial truth of a sentence in a partial structure is equivalent to the truth of that sentence in an expansion of a structure that corresponds naturally to the partial structure. Further, a mapping is a partial homomorphism/partial isomorphism between two partial structures if and only if it is a homomorphism/isomorphism between their corresponding structures. It is a corollary that the partial truth of a sentence in a partial structure is equivalent to the truth of a specific (...) Ramsey sentence in a corresponding structure. Hence the partial structures approach can be expressed in standard first or second-order model theory, and it can be captured in the received view on scientific theories as developed by Carnap and Hempel. (shrink)

Il saggio muove da una ricostruzione storico-concettuale dell’interpretazione merleau-pontyana del manoscritto di Husserl Rovesciamento della dottrina copernicana nell’interpretazione della corrente visione del mondo, con cui Merleau-Ponty è in dialogo sin dalla Fenomenologia della percezione, per ripercorrere gli sviluppi del tema della Terra nell’avanzare della riflessione merleau-pontyana sul corpo-proprio, sull’organismo vivente, sulla dimensione carnale dell’essere. La proposta di un ritorno alla Terra, intesa come Boden irriducibile dell’esperienza, trova infatti il suo risvolto ontologico nell’idea di Spielraum, che già Husserl definiva come “ambito (...) di possibilità”, e che in Merleau-Ponty assume il senso di un margine di gioco sempre aperto nella carne. Boden e Spielraum, non a caso tematizzati da Merleau-Ponty in due corsi paralleli tenuti al Collège de France nell’anno 1959-1960, permettono una rivalutazione del vivente secondo un modello che, contro il riduzionismo meccanicista, privilegi la spontaneità e la contingenza, e aprono allo sviluppo dell’ontologia porosa che il filosofo andrà proponendo negli ultimi anni. Ricostruendo la funzione della riflessione sulla corporeità e sul rapporto del vivente al mondo-ambiente in questa maturazione, si argomenterà che la critica che Merleau-Ponty muove al dualismo empirismo-idealismo trovi nell’idea di Terra un momento chiave, che contribuisce ad orientarla in direzione di una filosofia della carne. Questo passaggio riconfigura la Natura stessa, pensata non già come un originario, ma in quanto ambito di possibilità processuale e transindividuale, come quel quasi-oggetto, come lo definiva, ancora, Husserl, che presenta un’irriducibile resistenza ad un pensiero di sorvolo, proprio in quanto è condizione del pensiero stesso e ancoraggio della vita tutta.This essay begins with a historico-conceptual reconstruction of the Merleau-Pontian interpretation of Husserl’s manuscript, “Foundational Investigations of the Phenomenological Origin of the Spatiality of Nature,” with which Merleau-Ponty is in dialogue from Phenomenology of Perception onward, and revisits the development of the theme of the Earth in the progression of Merleau-Ponty’s reflection on le corps propre, the living organism, and the carnal dimension of being. The proposal for a return to the Earth, taken as irreducible Boden of experience, indeed finds its ontological reverse side in the idea of Spielraum, which Husserl already defined as a “milieu of possibilities,” and which in Merleau-Ponty takes on the sense of a margin of play always open in the flesh. Boden and Spielraum, two notions that Merleau-Ponty does not thematize by chance in the two parallel courses given at the Collège de France over the years 1959-1960, enable a reassessment of the living being according to a model that, against mechanistic reductionism, privileges spontaneity and contingency, and opens to the development of the porous ontology that the philosopher would propose in his final years. Reconstructing the function of reflection on corporeality, and on the relationship of the living being with its milieu in the process, it will be argued that the criticism directed by Merleau-Ponty against the dualism of empiricism-idealism finds in the idea of the Earth a key moment that contributes to orienting him in the direction of a philosophy of the flesh. This passage reconfigures Nature itself, no longer conceived of as an originating, but as a milieu of processual and transindividual possibilities, like that quasi-object, as Husserl again defined it, that presents an irreducible resistance against high-altitude thinking, precisely as the condition of thought itself and the anchorage of all life.Cet essai commence avec une reconstruction historico-conceptuelle de l’interprétation merleau-pontienne du manuscrit de Husserl, Renversement de la doctrine copernicienne, avec lequel Merleau-Ponty est en dialogue depuis la Phénoménologie de la perception, et revisite les développement du thème de la Terre dans la progression de la réflexion merleau-pontienne sur le corps propre, sur l’organisme vivant, sur la dimension charnelle de l’être. La proposition d’un retour à la Terre, prise comme Boden irréductible de l’expérience, trouve en effet son envers ontologique dans l’idée de Spielraum, que Husserl déjà définissait comme « milieu de possibilités » et qui chez Merleau-Ponty prend le sens d’une marge de jeu toujours ouverte dans la chair. Boden et Spielraum, deux notions que Merleau-Ponty ne thématise pas par hasard dans les deux cours parallèles donnés au Collège de France au cours de l’année 1959-1960, permettent une réévaluation du vivant selon un modèle qui, contre le réductionnisme mécaniste, privilégie la spontanéité et la contingence, et ouvrent au développement de l’ontologie poreuse que le philosophe allait proposer dans les dernières années. Reconstruisant la fonction de la réflexion sur la corporéité et sur le rapport du vivant avec son milieu dans ce processus, on argumentera que la critique dirigée par Merleau-Ponty contre le dualisme empirisme-idéalisme trouve dans l’idée de la Terre un moment clé qui contribue à l’orienter en direction d’une philosophie de la chair. Ce passage reconfigure la Nature elle-même, pensée non pas déjà comme un originaire, mais en tant que milieu de possibilités processuelles et transindividuelles, en tant que quasi-objet, comme le définissait, encore, Husserl qui offrait une résistance irréductible contre une pensée de survol, précisément en tant que condition de la pensée elle-même et ancrage de toute la vie. (shrink)

In the present paper, we return to one of the main theses we already defended concerning the role of the tarskian truth notion within the semantic approach (CARNIER, 2022). As it was argued, this truth notion proves to be insufficient to be applied to scientific theories as they are conceived by this approach, i.e., as extralinguistic entities, because it is a property of sentences and because the tarskian truth of a sentence doesn't necessarily mean the world is as it describes, (...) which results in the fact that other truth conceptions more appropriate need to be articulated within the several members of the semanticist family, in order to characterize the relationship between theory and phenomenon. Our argument in this regard was based in a case study applied to constructive empiricism and quasi-realism, but in this paper we extend our analysis to structuralism, assuming and endorsing the position according to which this proposal may be considered a member of the semantic approach. (shrink)

Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support, they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present four arguments to the effect that non-deductive evidence can yield knowledge of a mathematical proposition. We also show (...) that some of what mathematicians take to be deductive knowledge is in fact non-deductive. 1 Introduction2 Why It Might Matter3 Two Further Examples and Preliminaries4 An Exclusive Epistemic Virtue of Proof?5 Analyses of Knowledge6 The Inductive Basis of Deduction7 Physical to Mathematical Linkages8 Conclusion. (shrink)

The paper aims to explain and illustrate why Einstein and Kant, relativity and transcendental idealism, came to be discussed in one breath after the Special theory of relativity had emerged in 1905. There are essentially three points of contact between the theory of relativity and Kant's objective idealism. The Special theory makes contact with Kantian views of time; the General theory requires a non-Kantian view of geometry; but both relativity theories endorse a quasi-Kantian view of the nature of scientific (...) knowledge. The paper shows that Einstein is a Kantian in his insistence on the synthesis of rationalism and empiricism, but not in the details of his physics. (shrink)

Pierre Gassendi (b. 1592, d. 1655) was a French philosopher, scientific chronicler, observer, and experimentalist, scholar of ancient texts and debates, and active participant in contemporary deliberations of the first half of the seventeenth century. His significance in early modern thought has in recent years been rediscovered and explored, towards a better understanding of the dawn of modern empiricism, the mechanical philosophy, and relations of modern philosophy to ancient and medieval discussions. Through an arch-empiricism—tempered by adherence to key (...) elements of Church doctrine—Gassendi views metaphysics as a realm for speculation grounded in the possibility of empirical confirmation, logic as a psychologistic and probabilistic enterprise, knowledge of the external world as built on and subject to sensory-based evidence, and ethics in quasi-hedonist, possibly quantifiable terms. His philosophy is a constant review of other sources, a thorough consideration of the landscape into which his own empiricism fits and represents an alternative to contrasting claims, past and present. Other hallmarks of his thought include an atomist matter theory, explorations and defenses of the new physics, objections to the Meditations, and refutations of contemporary Aristotelians and mystical thinkers. His presentation of an empiricism, atomism, and new cosmology in historical and philosophical context greatly advanced the community of scholarship in his day, and represents a then-new model of research and exposition. (shrink)

This chapter is concerned only with some of the conceptual (or philosophical) issues relevant to the innateness hypothesis: the supposed analogy with Rationalists’ concern with mathematics; the false contrast between innate and learned; and the character of general statistical (GenStat) approaches. It is not so easy, however, to deal with a Leibnizian problem of the modal status of grammatical rules, nor with a little‐noticed problem, ironically enough raised by the modern empiricist Quine, what the author call superficialism regarding the data (...) available to the child. The chapter shows that a consideration of these problems will invite a specific form of nativism, what might be called a “quasi‐brute process” nativism, that is actually not as closely related to traditional Rationalism as Chomsky originally proposed, but is what he and others have arguably had in mind since the development of the Principles and Parameters and other “biological” models beginning in the 1970s. (shrink)

This essay introduces two leading Finnish philosophers of the twentieth century, Eino Kaila and Georg Henrik von Wright, who not only established analytic philosophy in Finland but also made original contributions to the development of pragmatism. The pragmatist dimensions of Kaila’s thought were clearly influenced by the classical American pragmatists, primarily William James, whose writings Kaila read and commented on already at an early stage of his career in the 1910s. Kaila then continued to develop a quasi-pragmatist idea of (...) “practical testability” during his logical empiricist period in the 1930s and 1940s. Unlike Kaila, von Wright was never directly inspired by James or any other classical pragmatists, although he did refer to Peirce and James as informal precursors of logical empiricism in the 1940s. His highly original theories of human action and causation, mostly developed in the 1970s, contain interesting pragmatist aspects, however. Both Kaila and von Wright, moreover, shared a life-long engagement with an issue that also troubled all the classical pragmatists: a reconciliation of a “humanist” philosophy with a thoroughgoing appreciation of the natural sciences. Thus, they both developed non-reductive versions of naturalism (or naturalist versions of pragmatist humanism) that, in their emphasis on the disunity of science, were not terribly far from the positions of classical pragmatists like James and Dewey. (shrink)

In this paper, I focus on an internal tension within James’s Principles and suggest that its formal structure provides useful insight into James’s subsequent evolution. Specifically, through a close reading of James’s account of ‘conceptions’ in the Principles, I examine the tension between these ‘conceptions’ construed as discrete and self-identical and James’s famous phenomenological description of consciousness as a continuous stream. Such a tension primarily involves the intersection of an epistemic need (or condition of possibility) with a quasi-metaphysical intuition (...) or postulate (continuity). Importantly, this tension is intensified by the methodological constraints of bracketing metaphysical questions which James sets for himself in the Principles. James’s decision to deny the cogency of this methodological bracketing can therefore be read as his response to the tension I examine and his speculative turn to “radical empiricism” as an attempt to resolve epistemological difficulties by going more radical ontologically. Doing so raises questions about the status of speculative metaphysics in intersection with empirical inquiry. (shrink)

This article examines Hilary Putnam's work in the philosophy of mathematics and - more specifically - his arguments against mathematical realism or objectivism. These include a wide range of considerations, from Gödel's incompleteness-theorem and the limits of axiomatic set-theory as formalised in the Löwenheim-Skolem proof to Wittgenstein's sceptical thoughts about rule-following, Michael Dummett's anti-realist philosophy of mathematics, and certain problems – as Putnam sees them – with the conceptual foundations of Peano arithmetic. He also adopts a thought-experimental approach – a (...) variant of Descartes' dream scenario – in order to establish the in-principle possibility that we might be deceived by the apparent self-evidence of basic arithmetical truths or that it might be ‘rational’ to doubt them under some conceivable set of circumstances. Thus Putnam assumes that mathematical realism involves a self-contradictory ‘Platonist’ idea of our somehow having quasi-perceptual epistemic ‘contact’ with truths that in their very nature transcend the utmost reach of human cognitive grasp. On this account, quite simply, ‘nothing works’ in philosophy of mathematics since wecan either cling to that unworkable notion of objective truth or abandon mathematical realism in favour of a verificationist approach that restricts the range of admissible statements to those for which we happen to possess some means of proof or ascertainment. My essay puts the case, conversely, that these hyperbolic doubts are not forced upon us but result from a false understanding of mathematical realism – a curious mixture of idealist and empiricist themes – which effectively skews the debate toward a preordained sceptical conclusion. I then go on to mount a defence of mathematical realism with reference to recent work in this field and also to indicate some problems – as I seethem – with Putnam's thought-experimental approach as well ashis use of anti-realist arguments from Dummett, Kripke, Wittgenstein, and others. (shrink)

In the paper I consider the prospects of interpreting late Carnap view on ontology as being in part a sort of fictionalism. More precisely, I argue that the theses he maintained in the volume of The Library of Living Philosophers devoted to his philosophy , in which he concerned with semantics in general and the confirmation of existential claims, make his account of an ontologically uncommittal acceptance of existential claims, as presented in his Empiricism, Semantics, and Ontology , unsatisfying. (...) In this work, he claimed that – to put it roughly – one can accept existential claims as true relatively to rules that constitue the linguistic framework in which these claims are formulated and that from the truth relative to these rules one can’t derive any conclusion about the objective truth of these existential claims. But in the volume of The Library of Living Philosophers he adopted a new view on the nature of semantic values and took them to be extralinguistic entities. This change forced him to redefine the notion of being true relative to rules of the liguistic framework in terms of being true in admissible models of this language, where a model is an ad-missible model of a given language, if all meaning postulates of this language are satisfied in that model. This change of the view calls for an explanation of how it is possible to take some existential claims to be true in a model without accepting the existence of entities in the domain of that model. Following S. Yablo’s view ex-pressed in his Does Ontology Rest on Mistake , I suggest that one can accept the thesis that existential claims are satisfied by some extralinguistic entities in some model in a spirit of make-believe in which one makes supposition that there are such enti-ties and that they satisfy these existential claims. I also argue against propositions of interpreting Carnap as a quasi-realist on the ground that this kind of interpretation doesn’t give a justice to the distinction between internal existential claims and prag-matic external existential claims, i.e. those claims that should be treated as claims about pragmatic values of a given linguistic framework. (shrink)

The main thesis defended in this paper is that Hildebrand’s distinction between what we could call quiddities—or “quasi-essences,” endowed with chaotic and accidental unity—and genuine essences possessing an intrinsically necessary unity, grounds the radical distinction between analytic and synthetic a priori knowledge. This thesis has not been expressly emphasized by Hildebrand himself. In order to prove it, we: (1) relate the three types of unities distinguished by Hildebrand with the three kinds of judgments discriminated by Kant; (2) outline what (...) we can call the “crux of empiricism”; (3) analyze four characteristic examples of synthetic a priori judgements; and (4) elaborate a provisional typology of synthetic a priori propositions, trying to include in it Hildebrand’s favorite examples. (shrink)

The main thesis defended in this paper is that Hildebrand’s distinction between what we could call quiddities—or “quasi-essences,” endowed with chaotic and accidental unity—and genuine essences possessing an intrinsically necessary unity, grounds the radical distinction between analytic and synthetic a priori knowledge. This thesis has not been expressly emphasized by Hildebrand himself. In order to prove it, we: relate the three types of unities distinguished by Hildebrand with the three kinds of judgments discriminated by Kant; outline what we can (...) call the “crux of empiricism”; analyze four characteristic examples of synthetic a priori judgements; and elaborate a provisional typology of synthetic a priori propositions, trying to include in it Hildebrand’s favorite examples. (shrink)

⦿ In my dissertation I introduce, motivate and take the first steps in the implementation of, the project of naturalising modal metaphysics: the transformation of the field into a chapter of the philosophy of science rather than speculative, autonomous metaphysics. -/- ⦿ In the introduction, I explain the concept of naturalisation that I apply throughout the dissertation, which I argue to be an improvement on Ladyman and Ross' proposal for naturalised metaphysics. I also object to Williamson's proposal that modal metaphysics (...) --- or some view in the area --- is already a quasi-scientific discipline. -/- ⦿ Recently, some philosophers have argued that the notion of metaphysical modality is as ill defined as to be of little theoretical utility. In the second chapter I intend to contribute to such skepticism. First, I observe that each of the proposed marks of the concept, except for factivity, is highly controversial; thus, its logical structure is deeply obscure. With the failure of the "first principles" approach, I examine the paradigmatic intended applications of the concept, and argue that each makes it a device for a very specific and controversial project: a device, therefore, for which a naturalist will find no use for. I conclude that there is no well-defined or theoretically useful notion of objective necessity other than logical or physical necessity, and I suggest that naturalising modal metaphysics can provide more stable methodological foundations. -/- ⦿ In the third chapter I answer a possible objection against the in-principle viability of the project: that the concept of metaphysical modality cannot be understood through the philosophical analysis of any scientific theory, since metaphysical necessity "transcends'' natural necessity, and science only deals with the latter. I argue that the most important arguments for this transcendence thesis fail or face problems that, as of today, remain unsolved. -/- ⦿ Call the idea that science doesn't need modality, "demodalism''. Demodalism is a first step in a naturalistic argument for modal antirealism. In the fourth chapter I examine six versions of demodalism to explain why a family of formalisms, that I call "spaces of possibility'', are (i) used in a quasi-ubiquitous way in mathematised sciences (I provide examples from theoretical computer science to microeconomics), (ii) scientifically interpreted in modal terms, and (iii) used for at least six important tasks: (1) defining laws and theories; (2) defining important concepts from different sciences (I give several examples); (3) making essential classifications; (4) providing different types of explanations; (5) providing the connection between theory and statistics, and (6) understanding the transition between a theory and its successor (as is the case with quantisation). -/- ⦿ In fifth chapter I propose and defend a naturalised modal ontology. This is a realism about modal structure: my realism about constraints. The modal structure of a system are the relationships between its possible states and between its possible states and those of other systems. It is given by the plurality of restrictions to which said system is subject. A constraint is a factor that explains the impossibility of a class of states; I explain this concept further. First, I defend my point of view by rejecting some of its main rivals: constructive empiricism, Humean conventionalism, and wave function realism, as they fail to make sense of quantum chaos. This is because the field requires the notion of objective modal structure, and the mentioned views have trouble explaining the modal facts of quantum dynamics. Then, I argue that constraint realism supersedes these views in the context of Bohm's standard theory and mechanics, and underpins the study of quantum chaos. Finally, I consider and reject two possible problems for my point of view. -/- ⦿ A central concern of modal metaphysicians has been to understand the logical system that best characterises necessity. In the sixth chapter I intend to recover the logical project applied to my naturalistic modal metaphysics. Scientists and philosophers of science accept different degrees of physical necessity, ranging from purely mathematically necessary facts that restrict physical behaviour, to kinetic principles, to particular dynamical constraints. I argue that this motivates a multimodal approach to modal logic, and that the time dependence of dynamics motivates a logic of historical necessity. I propose multimodal propositional (classical) logics for Bohmian mechanics and the Everettian theory of many divergent worlds, and I close with a criticism of Williamson's approach to the logic of state spaces of dynamic systems. (shrink)

Critics from the Nordic countries played a significant role in the development of the philosophies of the Vienna Circle. By the time the first English-language monograph-length critical study of Viennese neopositivism was published—as well as A. J. Ayer’s Language, Truth and Logic —several critical studies by philosophers from Sweden and Finland were already gathering dust: Eino Kaila’s Der logische Neupositivismus , Åke Petzäll’s Logistischer Positivismus and his Zum Methodenproblem der Erkenntnislehre . With their authors having participated in the meetings of (...) the Circle, these early monographs mirror the development of Viennese neopositivism as few other critical monographs do. Kaila focussed on the philosophical methodology and the doctrines adopted in Carnap’s Der logische Aufbau der Welt . His arguments were discussed in the Circle’s meetings and Carnap published a friendly review in which he nevertheless rejected Kaila’s criticisms, in particular of the method of quasi-analysis. Petzäll also seems to have regarded an Aufbau-style Konstitutionssystem as the ideal type of Viennese neopositivism, but he rather focussed on the difficulties to find a version of the empiricist meaning criterion that not only all members of the Vienna Circle could agree to, but also was able to withstand critical attention. His first monograph reached the sceptical conclusion that verificationism was caught in a paradox. (shrink)

In their Minds and Machines essay How would you know if you synthesized a Thinking Thing? (Kary & Mahner, Minds and Machines, 12(1), 61–86, 2002), Kary and Mahner have chosen to occupy a high ground of materialism and empiricism from which to attack the philosophical and methodological positions of believers in artificial intelligence (AI) and artificial life (AL). In this review I discuss some of their main arguments as well as their philosophical foundations. Their central argument: ‘AI is Platonism’, (...) which is based on a particular interpretation of the notion of ‘definition’ and used as a critique against AI, can be counter criticized from two directions: first, Anti-Platonism is not a necessary precondition for criticizing AI, because outspoken Platonist criticism against AI is already known (Penrose, The emperor’s new mind (with a foreword by M. Gardner), 1989). Second, even in case that AI would essentially be ‘Platonism’ this would not be a sufficient argument for proving AI wrong. In my counter criticism I assume a more or less Popperian position by emphasizing the openness of the future: Not by quasi-Scholastic arguments (like Kary and Mahner’s), but only after being confronted with a novel ‘thinking thing’ by future AI engineers we can start to analyze its particular properties (Let me use a history analogon to illustrate my position: In the 19th century, mechanized aviation was widely regarded impossible—only natural organisms (such as birds or bees) could fly, and any science of aerodynamics or aviation did not exist. Only after some non-scientific technicians had confronted their astonished fellows with the first (obviously) flying machine the science of ‘Artificial Aviation’ came into existence, motivated by the need for understanding and mastering that challenging and puzzling new phenomenon). (shrink)

According to Kant, arithmetic judgements are not analytic since they are about our practice of operating with figures and things in a certain way. Hence the empiricist thesis that any meaningful assertion is either analytic or synthetic a posteriori seems to be refuted (§§ 1, 2). Using syntax and semantics of truth-conditional logic Frege nevertheless shows that arithmetic can be understood as a system of quasi-analytic sentences speaking about numbers as abstract entities (§§ 3, 4). Axiomatic set theory, however, (...) conceals the connection between (internal) truth-functional arithmetic and our (external) practice of counting and computing (§§ 5-€“7). ---” In spite of the insights truth-conditional semantics provides for a non-psychological understanding of mathematical thinking, it is neither a general theory of meaning and analyticity nor a foundation of a general sense-criterion (§§ 8, 9). (shrink)