A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted (...) rather a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

In this paper I intend to grapple with the idea of philosophy as rigorous science from the point of view of Husserl‟s phenomenology in order to show that this idea may have an important contribution to the way in which the scientific character of sciences in general, and of human and social sciences in particular, is being conceived. As rigorous science, phenomenology emphasizes and investigates the a priori context of other sciences. In this way, it plays (...) a vital role in the development of every particular eidetic upon which any sciences rely. This eidetic (or the eidetic layer of any mature science) embraces the goal and strives to reach the objective of determining the valid sense of the fundamental notions used by the scientist in his research, without, nevertheless, stirring a radical questioning of this sense and of the ultimate validity of these notions. To define them requires passing from the usual level of inquiring of that particular science (the processes of dealing with facts and experiments) to the level (or meta-level) of a radical reflection on the sense or the meaning of the basic notions of the science in question (its own foundations). Philosophy as rigorous science connects the researcher´s assertions not only to the empirical state of affairs envisaged by his work, but, moreover and in a fundamental way, to their noematic content, to their intrinsic intentional meaning. Therefore, the idea of rigorous science elaborated in Husserl‟s phenomenology is heavy with the potential of clarifying the foundations and stakes of the research undertaken by the other sciences. (shrink)

It is difficult to imagine that a Royal Institute of Physics would organize an annual lecture series on the theme ‘conceptions of physics’. Similarly, it is quite improbable that a Royal Institute of Astronomy would even contemplate inviting speakers for a lecture series called ‘conceptions of astronomy’. What, then, is so special about philosophy that the theme of this lecture series does not appear to be altogether outlandish? Is it, perhaps, that philosophy is the reflective discipline par excellence, so that (...) the very nature of philosophy is a topic that belongs to its domain of investigations? Or is there something more serious at issue? Let me first tell you how the question concerning the nature of philosophy arose for me as a young student, and how I tried to answer it, quite naively, by endorsing Edmund Husserl's programme of turning philosophy into a rigorous science. In a second section, I shall offer three diagnoses of the fact that all such attempts seem to have failed. Finally, I'd like to say a few words on my own research agenda in philosophy and on a public function of philosophers. (shrink)

Resumen: El artículo analiza los escritos de Heidegger de 1911 sobre el “juramento modernista” exigido por Pío X. En la discusión de Heidegger con el liberalismo encontramos tensiones políticas que se mantienen hasta nuestros días. La separación efectiva entre Iglesia y Estado, la pretensión de una educación laica, el rol neutro de un Estado al que grupos ultraconservadores acusan de parcial e ideológico, son algunos de los problemas que aparecen en esta polémica.: The article analyzes Heidegger's 1911 writings on the (...) "modernist oath" demanded by Pius X. Heidegger's quarrel with liberalism exposes some political tensions that continues nowadays. The effective separation between church and state, the aim of a secular education, the neutral role of a state that ultraconservative groups accuse of being biased and ideological, are some of the problems that appear in this controversy. (shrink)

Husserl (a mathematician by education) remained a few famous and notable philosophical “slogans” along with his innovative doctrine of phenomenology directed to transcend “reality” in a more general essence underlying both “body” and “mind” (after Descartes) and called sometimes “ontology” (terminologically following his notorious assistant Heidegger). Then, Husserl’s tradition can be tracked as an idea for philosophy to be reinterpreted in a way to be both generalized and mathenatizable in the final analysis. The paper offers a pattern borrowed from the (...) theory of information and quantum information (therefore relating philosophy to both mathematics and physics) to formalize logically a few key concepts of Husserl’s phenomenology such as “epoché” “eidetic, phenomenological, and transcendental reductions” as well as the identification of “phenomenological, transcendental, and psychological reductions” in a way allowing for that identification to be continued to “eidetic reduction” (and thus to mathematics). The approach is tested by an independent and earlier idea of Husserl, “logical arithmetic” (parallelly implemented in mathematics by Whitehead and Russell’s Principia) as what “Hilbert arithmetic” generalizing Peano arithmetics is interpreted. A basic conclusion states for the unification of philosophy, mathematics, and physics in their foundations and fundamentals to be the Husserl tradition both tracked to its origin (in the being itself after Heidegger or after Husserl’s “zu Sache selbst”) and embodied in the development of human cognition in the third millennium. (shrink)

Edmund Husserl, the founder of modern phenomenology, always insisted that philosophy is not just a scholarly discipline, but can and must aspire to the status of a ‘strict’ or ‘rigorous science’ (strenge Wissenschaft). Heidegger, by contrast, began his winter lectures in 1929 by dismissing what he called the ‘delusion’ that philosophy was or could be either a discipline or a science as the most disastrous debasement of its innermost essence. To understand what Husserl had in mind, it (...) is important to begin by remembering that the word Wissenschaft has a wider extension than the word ‘science’. German distinguishes the Naturwissenschaften from the Geisteswissenschaften, or human sciences, which Husserl and Heidegger both believed could be perfectly ‘rigorous’ in their own way. Speakers of English, by contrast, tend to draw a threefold distinction among the natural sciences, the social sciences, and the humanities. (shrink)

Abstract: Brentano’s conception of scientific philosophy had a strong influence on his students and on the intellectual atmosphere of Vienna in the late nineteenth century. The aim of this article is to expose Brentano’s conception and to contrast his views with that of two traditions he is said to have considerably influenced: phenomenology and analytic philosophy. I will shed light on the question of how and to what extent Brentano’s conception of philosophy as a rigorous science has had (...) an impact on these two traditions. The discussion will show that both took their liberties in the interpretation of the thesis, a move that allowed them to liberate themselves from Brentano’s inheritance and to fully develop their own philosophical positions. (shrink)

Johann Wolfgang von Goethe's approach to natural scientific research has unmistakable parallels to phenomenology. These parallels are clear enough to allow one to say confidently that Goethe's delicate empiricism is indeed a phenomenology of nature. This paper examines how Goethe's criticisms of Newton anticipated Husserl's announcement of the crisis of the modern sciences, and it describes how Goethe, at a critical juncture in cultural history, addressed this emerging crisis through a scientific method that is virtually identical to the method of (...) contemporary empirical-phenomenological research in the human sciences. Goethe's practice of science shares with phenomenology a participatory, morally-responsive, and holistic approach to the description of dynamic life-world phenomena. Delicate empiricism has its own version of the phenomenological epoché, and, like Husserl's technique of imaginative variation, it strives to disclose the essential or archetypal structure of the phenomenon through the endowment of human imagination. However, a close reading of Goethe suggests that the tendency amongst some scholars to distinguish phenomenology as human science from the natural sciences is actually a costly error which unwittingly falls prey to implicit Cartesian assumptions. Goethe, however, manages to avoid these problems by performing from the first a phenomenology of nature's sensibility. (shrink)

RESUMEN Husserl se esforzò por desarrollar vías de abordaje a la fenomenología que facilitaran su expansión. En "La filosofía como ciencia estricta" traza un diagnóstico de los obstáculos en el entramado de naturalismo e historicismo, y estudia su lógica de construcción a través de tres tópicos: apelación al psicologismo como elemento del naturalismo, interpretación de Hume como protofenomenólogo y lectura historicista de Dilthey. Esto permitirá observar datos relevantes sobre el modo como Husserl concibe en este período la especificidad y alcances (...) de la fenomenología. ABSTRACT Husserl endeavored to develop approaches to phenomenology that would facilitate its expansion. In "Philosophy as Rigorous Science", he provides a diagnosis of the obstacles found in the interweaving of naturalism and historicism, and analyzes the logic of its construction by means of three themes: the appeal to psychologism as an element of naturalism, the interpretation of Hume as a proto-phenomenologist, and the historicist reading of Dilthey. This makes it possible to obtain relevant information regarding the manner in which Husserl conceived the specificity and scope of phenomenology during that period. (shrink)

In this widely hailed and long out of print classic of twentieth-century philo-sophic commentary, Farber explains the origin, development, and function of ...

Hegel sees philosophy as the only rigorous science that does not have any presupposition, but he rejects the possibility of an absolute foundation for philosophy, instead maintaining that only the system as a whole can be free from all presuppositions. Hegel’s system lays claim to presuppositionlessness, not on the ground of any presuppositionless beginning, but rather as a holistic system of concepts in which inevitable presuppositions are made transparent and comprehended. This paper examines Hegel’s analysis of the concept (...) of immediacy and his critique of the foundationalist conception of philosophy. Although Hegel’s critique is targeted against his predecessors and contemporaries, it has important implications for Husserl’s phenomenology, which represents one of the most ambitious foundationalist projects in the history of philosophy. The final part discusses the later development of Husserl’s thought and his introduction of the concept of lifeworld in light of Hegel’s critique. (shrink)

In this widely hailed and long out of print classic of twentieth century philosophic commentary, Professor Farber explains the origin, development, and function of phenomenology with a view towards its significance for philosophy in general. The book offers a general account of Husserl and the background of his philosophy. The early chapters are devoted to his mathematical-philosophical and psychological studies. The refutation of psychologism is present in detail, together with the critical reaction to it. The development of his logical theories (...) in the light of contemporary literature at the close of the 19th century is next considered. The main content of the six Logical Investigations follows, which contribute to the phenomenological elucidation of experience and knowledge. The phenomenological philosophy of logic as developed in Husserl's later writings is then introduced, followed by a discussion of the phenomenological method and its proper function. Farber makes clear his preference for phenomenology as a purely descriptive method and his opposition to have it serve as a last stronghold of metaphysics. Indispensable as groundwork for descriptive philosophical study, this book will deeply interest not only serious students of philosophy and psychology, but also those who are concerned with the philosophical aspects of mathematics, social and natural sciences, law and psychiatry. (shrink)

In questo articolo intendo presentare e discutere le tesi avanzate da Husserl contro il naturalismo epistemologico e psicologico in La filosofia come scienza rigorosa. Intendo mostrare come la sua critica si rivolga a posizioni generalmente più estreme rispetto alle varianti del naturalismo oggi dibattute; e tuttavia le tesi husserliane hanno implicazioni interessanti per la discussione contemporanea. In primo luogo, egli mostra come vi sia un nesso importante tra naturalismo epistemologico e naturalismo psicologico. In secondo luogo, egli mostra come una versione (...) robusta di naturalismo epistemologico indebolisca se stesso, non riuscendo a traslare la cogenza logica in termini psicologici. In terzo luogo – e questo è il tratto più importante per la discussione contemporanea – egli attacca il cartesianesimo in quanto forma di naturalismo psicologico per via del considerare la psiche come sostanza. Contro questa posizione Husserl afferma la necessità di formulare nuovi obiettivi epistemici per le ricerche sulla coscienza, sostenendo che il fattore di maggiore interesse circa la coscienza non sia la sua fatticità empirica, bensì la sua funzione trascendentale, che garantisce accesso conoscitivo a ogni tipo di oggetto. Lo studio di questa funzione richiede un metodo specifico, da non confondersi con i metodi empirici. Nella parte conclusiva intendo sostenere come le analisi husserliane offrano nuove prospettive sulla struttura della coscienza, di cui oggi si sente il bisogno, ma anche argomenti persuasivi contro le incerte speculazioni metafisiche circa il rapporto tra mente e corpo. (shrink)

American taxpayers spend $30 billion annually funding biomedical research. By some estimates, half of the results from these studies can't be replicated elsewhere-the science is simply wrong. Often, research institutes and academia emphasize publishing results over getting the right answers, incentivizing poor experimental design, improper methods, and sloppy statistics. Bad science doesn't just hold back medical progress, it can sign the equivalent of a death sentence. How are those with breast cancer helped when the cell on which 900 (...) papers are based turns out not to be a breast cancer cell at all? How effective could a new treatment for ALS be when it failed to cure even the mice it was initially tested on? In Rigor Mortis, award-winning science journalist Richard F. Harris reveals these urgent issues with vivid anecdotes, personal stories, and interviews with the nation's top biomedical researchers. We need to fix our dysfunctional biomedical system-now. (shrink)

Cartea pe care o prezentăm poate fi privită ca ilustrare a unei concepţii idealiste despre ştiinţă. Este meritul filozofului Edmund Husserl de a fi tulburat secolul trecut prin perseverenţa cu care a urmărit realizarea unei filozofii în formă riguroasă, ştiinţifică. Dacă sintagma în cauză a putut să apară pentru mulţi ca fiind nepotrivită pentru sensul şi posibilităţile filozofiei, lucrurile stau astfel şi pentru că filozofia gânditorului german a rămas pentru ei, într-o oarecare măsură, insondabilă. Voi susţine aici contrariul: ea este (...) o filozofie deschisă interpretării. (shrink)

A proof is given that there does not exist an event, that is not already in the past for some possible distant observer at the (our) moment that the latter is "now" for us. Such event is as "legally" past for that distant observer as is the moment five minutes ago on the sun for us (irrespective of the circumstance that the light of the sun cannot reach us in a period of five minutes). Only an extreme positivism: "that which (...) cannot yet be observed does not yet exist", can possibly withstand the conclusion concerned. Therefore, there is determinism, also in micro-physics. (shrink)

Critics of evolutionary psychology object that it is not rigorous science compared to other evolutionary science. Advocates reply that it is rigorous science, and that the critics are uninformed. Still, informed people having opposing preconceptions of what counts as rigor may reach opposing evaluative conclusions. I shall clarify the very idea of rigorous evolutionary histories in relation to the basic objection that “evolution without history” is not rigorous.

Against the modern tendency to considerate just the formal-empirical knowledge as Science, and this one mathematized as much as possible, here many declarations of Aristotle are raised in order to show that the scientific rigour is not univocal but analogic: it is determined according to the nature of the object to be known. This is a so elementary epistemological rule that not knowing it is understood by that philosopher as apaideusia, i.e., lack of basic education in the knowledge sphere (...) in general. To the Stagirite, a pepaideuménos, i.e., a well educated spirit requires to every subject just the kind of rigour which is adequate to it, attempting not to impose whether the demonstrative or the mathematical rigour to the subject. It is specially truth for the theological Science, whose subject, by being transcendent, asks for a sui generis rigour which has to be so faithful as possible to it. (shrink)

This paper argues that a successful philosophical analysis of models and simulations must accommodate an account of mathematically rigorous results. Such rigorous results may be thought of as genuinely model-specific contributions, which can neither be deduced from fundamental theory nor inferred from empirical data. Rigorous results provide new indirect ways of assessing the success of models and simulations and are crucial to understanding the connections between different models. This is most obvious in cases where rigorous results (...) map different models on to one another. Not only does this put constraints on the extent to which performance in specific empirical contexts may be regarded as the main touchstone of success in scientific modelling, it also allows for the transfer of warrant across different models. Mathematically rigorous results can thus come to be seen as not only strengthening the cohesion between scientific strategies of modelling and simulation, but also as offering new ways of indirect confirmation. (shrink)

Both early social psychologists and the modern, interdisciplinary scientific community have advocated for diverse team science. We echo this call and describe three common pitfalls of solo science illustrated by the target article. We discuss how a collaborative and inclusive approach to science can both help researchers avoid these pitfalls and pave the way for more rigorous and relevant research.

This paper critically examines and evaluates Yacin Hamami’s reconstruction of the standard view of mathematical rigor. We will argue that the reconstruction offered by Hamami is premised on a strong and controversial epistemological thesis and a strong and controversial thesis in the philosophy of mind. Secondly, we will argue that Hamami’s reconstruction of the standard view robs it of its original philosophical rationale, i.e. making sense of the notion of rigor in mathematical practice.

The ArgumentIt has long been apparent that in the nineteenth century, mathematics in France and England developed along different lines. The differences, which might well be labelled stylistic, are most easy to see on the foundational level. At first this may seem surprising because it is such a fundamental area, but, upon reflection, it is to be expected. Ultimately discussions about the foundations of mathematics turn on views about what mathematics is, and this is a question which is answered by (...) a variety of different groups including mathematicians, students, curricular planners, parents, etc. Mathematical practice rests on some kind of mixture of the answers to this fundamental question which come from these diverse groups. Comparing the cultural matrices which supported mathematics in France and Britain in the first decades of the nineteenth century sheds light on the real though often subtle differences in the ways the subject was pursued in the two countries. (shrink)

Open peer commentary on the article “Design Research as a Variety of Second-Order Cybernetic Practice” by Ben Sweeting. Upshot: I reflect on the theme of honesty in research and discuss the adjoining requirements of rigor from an academic perspective. Central to my discussion is Glanville’s assertion that what researchers - from either science or design - presented was not what they actually thought and did.

Until recently, the method of professional ethics has been largely principle-based. But the failure of this approach to take into sufficient account the character of professionals has led to a revival of virtue ethics. The kind of professional virtue ethics that I am concerned with in this paper is teleological in that it relates the virtues of a profession to the ends of this profession. My aim is to show how empirical research can be used to develop virtue-based accounts of (...) professional ethics, and that such empirically well-informed approaches are more convincing than traditional kinds of professional virtue ethics. The paper is divided into four sections. In the first, I outline the structure of a teleological approach to virtue ethics. In Section 2, I show that empirical research can play an essential role in professional ethics by emphasizing the difference between conceptual and empirical matters. Section 3 demonstrates the relevance of virtues in professional life; and the last section is concerned with some meta-ethical issues that are raised by a teleological account of professional virtues. (shrink)

Although the target article provides strong evidence against the locationist view, evidence for the constructionist view is inconclusive, because co-activation of brain regions does not necessarily imply connectivity between them. We propose a rigorous approach wherein connectivity between co-activated regions is first modeled using exploratory Granger causality, and then confirmed using dynamic causal modeling or Bayesian modeling.

The present paper examines the role of exact results in the theory of many‐body physics, and specifically the example of the Mermin‐Wagner theorem, a rigorous result concerning the absence of phase transitions in low‐dimensional systems. While the theorem has been shown to hold for a wide range of many‐body models, it is frequently ‘violated’ by results derived from the same models using numerical techniques. This raises the question of how scientists regulate their theoretical commitments in such cases, given that (...) the models, too, are often described as approximations to the underlying ‘full’ many‐body problem. (shrink)

"Mark Wilson aims to reconnect analytic philosophy with the evolving practicalities within science from which many of its grander concerns originally sprang. He offers an alternative history of how the subject might have developed had the insights of its philosopher/scientist forebears not been cast aside in the vain pursuit of 'ersatz rigor'"--.