The year 2023 celebrates the 125th anniversary of the birth of Mark Yakovlevich Vygodsky, a famous Soviet mathematician and pedagogue, one of the founders of the Soviet school of the history of mathematics. Not only the scientist's scientific achievements, but also his significant contribution to pedagogical theory and practice, allow us to describe him as a significant scientific figure of the twentieth century. His mathematics textbooks and reference books are reprinted almost annually, so that his ideas continue to influence educational (...) and scientific practice to this day. This article is the second in a series of publications prepared by the author, who is the great-grandson of M.Y. Vygodsky. This research presents previously unpublished scientific results and discoveries concerning the life and work of the scholar. Firstly, based on archival data and family memories, detailed facts about his origins, young years and his development as a scientist are presented. At the same time, a rather complete chronology of M.Y. Vygodsky's scientific activity and personal life is compiled. Secondly, for the first time, a complete list of his main scientific contributions has been prepared, which makes it possible to assess the talent and the scale of his academic achievements. The presented results may be useful for prospective scientific and historical studies. In the modern context, it seems valuable to present a picture of M.Y. Vygodsky's life and work, as he was an interdisciplinary researcher and in this he was ahead of his time. In our changing world, contemporary challenges require the same interdisciplinarity to solve complex problems, and a fresh look at the life and work of a scholar like M.J. Vygodsky can stimulate inspiration in the modern researcher, student, and anyone seeking development and awareness. (shrink)

The clash between Galileo and the Catholic Inquisition has been discussed, studied, and written about for many decades. The scientific, theological, political, and social implications have all been carefully analysed and appreciated in all their interpretative fruitfulness. The relatively recent trend in this kind of scholarship however seems to have underestimated the fact that Galileo in this debate, as in his earlier debates, showed a particular style marked by overconfidence. If we keep in mind the Lakatosian account (...) of scientific development, it is of course perfectly understandable that scientists at times stick to their convictions by producing auxiliary hypotheses as buffers against contrary evidence. And elements of this are detectable in the arguments of both Galileo and his opponents. But one still needs to ask: To what extent did Galileo depend on auxiliary hypotheses? How insecure did they render his position? And how ad hoc were they? These are important questions because Galileo’s particular way of dealing with auxiliary hypotheses can throw light on the broader question of when and how auxiliary hypotheses are needed within scientific practice in general. It can even indicate some way of conceiving degrees of ad hocness. In this paper, I explore this issue by comparing two important debates in which Galileo was involved: one about the nature of water and buoyancy, the other about cosmology. I revisit not only the scientific content of these debates but also the cultural context in which they took place, especially their dependence on patronage and their theological repercussions. The results indicate that scholarship on Galileo can still be useful in clarifying currently relevant aspects of scientific practice, and is thus still far from its expiry date. (shrink)

Far from egalitarian, Galileo’s epistemology asserts an uncompromising hierarchy between science and Scripture — an idea he suggests originates with early Christian author Tertullian of Carthage. For Galileo, when the scientific data causes us to disagree with the apparent meaning of scripture, it is not the data that we discard nor is it the scientist whose word is subject to doubt. Rather, whenever a disagreement arises, we always reinterpret the Bible and Holy Fathers such that we can make (...) them agree with what the scientist observes. Galileo states, “[H]aving arrived at any certainties in physics, we ought to utilize these as the most appropriate aids in the true exposition of the Bible […], for these must be concordant with demonstrated truths” (183). In other words, we establish matters of fact first , and then decide what interpretations of scripture will maintain the truth of those facts, second. Given that Galileo’s method stands in radical opposition to the methods of the Church as carried out in the Inquisition following the Council of Trent (1563), it is not hard to understand why the Church felt threatened by him and thereby sought to repress his views. (shrink)

Nobody expects the Scientific Inquisition!

The article focuses on Galileo's Letter to Castelli, 21 December 1613. The author analyzes Galileo's hermeneutical principles established in the first part of the letter and his literal interpretation of the passage from the Book of Joshua 10, 12-13, in Copernican terms, in the second part of the letter. Galileo appears to use the Bible as a scientific authority, supporting his Copernican views, and thus he seems to contradict his own hermeneutical principles. The author argues that (...) class='Hi'>Galileo's position is consistent, especially if one takes into account the historical context of its genesis, that is, in the context of the constant, theologically-inspired attacks on Copernicus and Galileo and his commitment to the heliocentric world system and in the context of his newly-made telescopic observations and discoveries. (shrink)

It is widely acknowledged that the Galilean Relativity Principle, according to which the laws of classical systems are the same in all inertial frames in relative motion, has played an important role in the development of modern physics. It is also commonly believed that this principle holds the key to answering why, for example, we do not notice the orbital velocity of the Earth as we go about our day. And yet, I argue in this paper that the precise content (...) of this principle is ambiguous: standard presentations, in both physics and philosophy, fail to distinguish between two principles that are ultimately inequivalent, the “External Galilean Relativity Principle” (EGRP) and the “Internal Galilean Relativity Principle” (IGRP). I demonstrate that EGRP and IGRP play distinct roles in physics practice (e.g., EGRP is connected to the concept of Galilean invariance, but IGRP is not) and that many classical systems that satisfy IGRP fail to satisfy EGRP. I further show that the Relativity Principle introduced by Einstein in 1905—which is not restricted to classical systems—also leads to two inequivalent principles, an external one analogous to EGRP, and an internal one analogous to IGRP. I conclude by noting that the phenomenon originally captured by Galileo’s famous ship passage is much more general than contemporary discussions in the philosophy of symmetries suggest. (shrink)

Galileo’s telescopic lunar observations, announced in Siderius Nuncius (1610), were a triumph of observational skill and ingenuity. Yet, unlike the Medicean stars, Galileo’s lunar “discoveries” were not especially novel. Indeed, Plutarch had noted the moon’s uneven surface in classical times, and many other renaissance observers had also turned their gaze moonward, even (in Harriot’s case) aided by telescopes of their own. Moreover, what Galileo and his contemporaries saw was colored by the assumptions they already had. Copernicans assumed (...) the moon was a terrestrial satellite, thus Galileo saw its mountains and Kepler “saw” the dwellings of its inhabitants. Aristotelians assumed the moon was a perfect sphere, so they saw differences in density and rarity in the lunar body. Theory corrected the results of observation, so Galileo’s lunar observations, like those that had come before, proved nothing. Yet this failure contained the germ of Galileo’s success, since the Siderius Nuncius gave observation a rhetorical force it did not have before. Observers on all sides set out to see for themselves what Galileo reported. Hence, all parties now had to answer to what they saw, whatever they believed. Thus, the Siderius Nuncius ultimately changed the grounds upon which natural philosophical argument and debate was carried out. In this new empirical arena, the Galilean science would eventually prevail. (shrink)

Girolamo Cardano makes a number of surprising, even shocking claims about the soul in his De subtilitate, one of the most widely read works of natural philosophy in the sixteenth century. When he was finally investigated by the Roman Inquisition and the Index, these claims did not go unnoticed. This study will narrow in on three passages marked as heretical by the first Holy Office censor of De subtilitate. It will consider the Inquisition’s priorities and ask about materialism, (...) determinism, and conceptual inconsistency in Cardano’s views on the soul. The study will give special attention to the claim made by Cardano that souls can be reduced to celestial heat. In addition to De subtilitate, several of Cardano’s other works will be considered for added perspective, especially Contradicentium medicorum libri duodecim. (shrink)

This paper proposes a reading of Galileo’s Letter to the Grand Duchess Christina as analogous to a legal brief submitted to a court en banc. The Letter develops a theory of the general issues underlying the case at hand, but it is organized around advocacy for a particular judgment. I have drawn two architectonic implications from this framework, each of which helps to resolve an issue still standing in the literature. First, the Letter anticipates varying degrees of acquiescence to (...) its general account, and provides ‘hooks’ for different readers to interpret variously while still converging on the particular judgment. This reading allows for a coherent Galilean interpretation of passages that notoriously concede priority to Scripture, while also explaining their dialectical function. Galileo is neither self-contradictory nor dissimulating here, but strategically leaves the specification of key distinctions for the reader. Second, the Letter, and particularly its apparent shifting of the burden of proof, must be understood in light of the tripartite ‘adversarial-judicial’ framework that Galileo sets up. The burden of proof is shifted to anti-Copernicans within the Church, not as a rhetorical trick, but because of the benefits of adversarial procedure that will accrue to the Church as the responsible judge. (shrink)

This study of the history and contents of a hitherto unedited work on geometry by Vincenzo Viviani seeks to present a picture of the scientific environment in Italy in the second half of the 17th century, with particular emphasis on Tuscany and the impact the condemnation of Galileo had on ongoing scholarship. Information derived from unedited or less well-known material serves to illuminate a range of prominent and marginal figures who adopted different strategies for the dissemination of Galileo’s (...) thought and the application of its principles. A selection of texts, edited here for the first time, is presented in two appendices, while in a third decidedly unusual methods are used to elucidate the mathematical aspects. (shrink)

The claim that Galileo Galilei transformed the spyglass into an astronomical instrument has never been disputed and is considered a historical fact. However, the question what was the procedure which Galileo followed is moot, for he did not disclose his research method. On the traditional view, Galileo was guided by experience, more precisely, systematized experience, which was current among northern Italian artisans and men of science. In other words, it was a trial-and-error procedure—no theory was involved. A (...) scientific analysis of the optical properties of Galileo’s first improved spyglass shows that his procedure could not have been an informed extension of the traditional optics of spectacles. We argue that most likely Galileo realized that the objective and the eyepiece form a system and proceeded accordingly. (shrink)

Was Galileo’s clash with the Church about science or about legal procedures that he had apparently neglected? Was he ultimately condemned for heresy or for violating a legal precept by publishing the "Dialogue on the Two Chief World Systems"?

ABSTRACT. In his Letters on the motion impressed by a moving mover, Gassendi offers a theory of the motion of composite bodies that closely follows Galileo’s. Elsewhere, he describes the motion of individual atoms in very different terms: individual atoms are always in motion, even when the body that contains them is at rest; atomic motion is discontinuous although the motion of composite bodies is at least apparently continuous; and atomic motion is grounded in an intrinsic vis motrix, motive (...) power, while composite bodies simply persist in their state of motion or rest in the absence of outside intereference. Gassendi does not make much effort to explain how his accounts of atomic and composite motion fit together, and it’s difficult to see how they could possible be integrated. My goal is to explain, given this difficulty, why he accepted both the Galilean theory of the motion of composite bodies and the Epicurean theory of atomic motion. (shrink)

We have a much better understanding of physics than we do of consciousness. I consider ways in which intrinsically mental aspects of fundamental ontology might induce modifications of the known laws of physics, or whether they could be relevant to accounting for consciousness if no such modifications exist. I suggest that our current knowledge of physics should make us skeptical of hypothetical modifications of the known rules, and that without such modifications it’s hard to imagine how intrinsically mental aspects could (...) play a useful explanatory role. Draft version of a paper submitted to Journal of Consciousness Studies, special issue responding to Philip Goff’s Galileo’s Error: Foundations for a New Science of Consciousness. (shrink)

There is an underappreciated respect in which the widespread availability of generative artificial intelligence (AI) models poses a threat to human connection. My central contention is that human creativity is especially capable of helping us connect to others in a valuable way, but the widespread availability of generative AI models reduces our incentives to engage in various sorts of creative work in the arts and sciences. I argue that creative endeavors must be motivated by curiosity, and so they must disclose (...) the creative agent’s inquisitive self. It is through self-disclosure, including the disclosure of the inquisitive self, that we put ourselves in a position to be seen by and connect with others through our creative pursuits. Because relying on AI for certain generative tasks is less self-disclosive than the creative work such technologies supplant, this reliance threatens to weaken our connections to one another. (shrink)

Brecht’s Life of Galileo provides elements for elaborating what I call “a theory of the encounter of practices”. The concept of the encounter pushes back against teleological theories that predestine modern science to operate as an instrument of domination. I argue that Life of Galileo stages the missed encounters in modernity between science, politics, and art at the same time as it foregrounds the emancipatory power of science. I trace the encounter of practices from the play’s opening scenes (...) – highlighting what I call Galileo’s “double life”. Then, I turn to the most important scene of the play, Scene 10, in which political and artistic practices repurpose Galileo’s novel inventions for their emancipatory desires. In the virtual potentialities of this encounter, that is, despite the missed encounter between Galileo and “the people”, Brecht’s Life of Galileo continues to be fruitful for theorizing the emancipatory power of science. (shrink)

This bookreview discusses Piccolino and Wades' book on Galileo's impact on contemporary perception science.

Working from within the Lakatosian framework of scientific change, this paper seeks to gain a deeper understanding of the Jesuits’ role in the scientific revolution during the years of Galileo’s trials and the subsequent century. Their received research program was Aristotelian cosmology. Their efforts to construct protective belts to shield the core principles were fueled not only by the basic instinct to conserve but also by the impact of official prohibitions from the side of Church authorities. The paper illustrates (...) how these Church restrictions were not as paralyzing for Jesuit intellectuals as has often been thought. They left considerable space for maneuvering. The paper shows how, within this space, Jesuits were engaged mainly in the indispensable task of exhausting all the potential of Aristotelian cosmology. They did this primarily by trying to build intellectual bridges to ensure coherence between three realms of the cosmological imagination of the time: the received Aristotelian view, the new empirical data, and the realm of everyday experience. (shrink)

We advance the understanding of the philosophy and psychology of curiosity by operationalizing and constructing an empirical measure of Nietzsche’s conception of inquisitive curiosity, expressed by the German term Wissbegier, (“thirst for knowledge” or “need/impetus to know”) and Neugier (“curiosity” or “inquisitiveness”). First, we show that existing empirical measures of curiosity do not tap the construct of inquisitive curiosity, though they may tap related constructs such as idle curiosity and phenomenological curiosity. Next, we map the concept of inquisitive curiosity and (...) connect it to related concepts, such as open-mindedness and intellectual humility. The bulk of the paper reports four studies: an Anglophone exploratory factor analysis, an Anglophone confirmatory factor analysis, an informant study, and a Germanophone exploratory and confirmatory factor analysis. (shrink)

Sometimes inquirers may rationally pursue a theory even when the available evidence does not favor that theory over others. Features of a theory that favor pursuing it are known as considerations of promise or pursuitworthiness. Examples of such reasons include that a theory is testable, that it has a useful associated analogy, and that it suggests new research and experiments. These reasons need not be evidence in favor of the theory. This raises the question: what kinds of reasons are provided (...) by pursuitworthiness considerations? Are they epistemic reasons or practical reasons? I argue that pursuitworthiness considerations are a kind of non-evidential epistemic reason, which I call an inquisitive reason. In support of this, I first point out two important similarities between the traditional pursuitworthiness considerations discussed in philosophy of science, which I call promise reasons, and certain social epistemic reasons that I call social inquisitive reasons. Specifically, both kinds of reason (1) favor pursuing a theory in a non-evidential way, and (2) concern promoting successful inquiry. I then propose recognition of a new category of normative reason: inquisitive reasons. This category contains both promise and social inquisitive reasons. Finally, I argue that inquisitive reasons share three essential features with previously recognized epistemic reasons: a connection to epistemic aims, explanatory independence, and the presence of a specific right-kind/wrong-kind reasons distinction. Each of these features have been used to argue that evidence should be treated as part of a distinct, independent domain of epistemic normativity. Since inquisitive reasons share these features, they too should be considered part of this independent epistemic domain. Thus, inquisitive reasons, including pursuitworthiness considerations, are epistemic reasons. (shrink)

This chapter contains section titled: Kepler's New Astronomy Kepler's New Science of Vision Galileo and the Telescope Galileo and the Creation of Mathematical Physics Mersenne and the New Science.

Starting with a discussion of what I call Koyré’s paradox of conceptual novelty, I introduce the ideas of Damerow et al. on the establishment of classical mechanics in Galileo’s work. I then argue that although the view of Damerow et al. on the nature of Galileo’s conceptual innovation is convincing, it misses an essential element: Galileo’s use of the experiments described in the first day of the Two New Sciences. I describe these experiments and analyze their function. (...) Central to my analysis is the idea that Galileo’s pendulum experiments serve to secure the reference of his theoretical models in actually occurring cases of free fall. In this way Galileo’s experiments constitute an essential part of the meaning of the new concepts of classical mechanics. (shrink)

Prawitz conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister. This article resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The paper further defines a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to allow double negation elimination (...) for atomic formulas and proves the extensional alignment of quasi-proof-theoretic validity and inquisitive logic. (shrink)

This chapter argues that the standard conception of Spinoza as a fellow-travelling mechanical philosopher and proto-scientific naturalist is misleading. It argues, first, that Spinoza’s account of the proper method for the study of nature presented in the Theological-Political Treatise (TTP) points away from the one commonly associated with the mechanical philosophy. Moreover, throughout his works Spinoza’s views on the very possibility of knowledge of nature are decidedly sceptical (as specified below). Third, in the seventeenth-century debates over proper methods in the (...) sciences, Spinoza sided with those that criticized the aspirations of those (the physico-mathematicians, Galileo, Huygens, Wallis, Wren, etc) who thought the application of mathematics to nature was the way to make progress. In particular, he offers grounds for doubting their confidence in the significance of measurement as well as their piece-meal methodology (see section 2). Along the way, this chapter offers a new interpretation of common notions in the context of treating Spinoza’s account of motion (see section 3). (shrink)

The mystery of the images and an unknown book.

The philosopher and his passion for the “gentle sex”.

Intellectual courage requires acting to promote epistemic goods despite significant risk of harm. Courage is distinguished from recklessness and cowardice because the expected epistemic benefit of a courageous action outweighs (in some sense) the threatened harm. Sometimes, however, inquirers pursue theories that are not best supported by their current evidence. For these inquirers, the expected epistemic benefit of their actions cannot be explained by appeal to their evidence alone. The probability of pursuing the true theory cannot contribute enough to the (...) expected epistemic benefit for the action to count as courageous rather than reckless. Thus, there must be some other epistemic consideration which favors their action, besides evidence for their theory. I argue that the proper account of intellectual courage requires recognition of inquisitive reasons: a distinct category of epistemic reasons which concern successful inquiry. This category includes reasons to think a theory itself is promising, e.g., that the theory suggests potentially fruitful new research. It also includes social epistemic reasons, e.g., that pursuing a theory will improve the distribution of cognitive labor. Inquisitive reasons help explain why researchers who pursue improbable theories count as intellectually courageous, rather than reckless. The expected epistemic benefit of an action is partially determined by the inquisitive reasons in its favor. On my account, intellectually courageous inquiry requires acting in a way that is sensitive to inquisitive reasons. (shrink)

For many years, the involvement of Jesuits in the development of science has stimulated curiosity and wonder. Is it true that the Society of Jesus was a serious impediment to the natural development of the scientific revolution during the sixteenth and seventeenth centuries?

The Fifth Element (1997) is a French science-fiction film in English, directed and co-written by Luc Besson. The title and the plot of the film refer to a central notion of Greek philosophy, that is, pemptousia, or quintessence. Pre-Socratic philosophers such as Thales, Anaxagoras, Anaximenes and others, were convinced that all natural beings – in fact, nature itself – consist in four primary imperishable elements or essences (ousiai), i.e., fire, earth, water, and air. To these four, Aristotle added aether, a (...) fifth essence (pemptousia). The introduction of aether gave birth to a great tradition in late Antique and Medieval philosophy, and eventually it came to signify not an additional primary element, but the core-essence of all beings, their fundamental ontological structure. Besson’s film draws its inspiration on this philosophical tradition but its cinematographic rendering of the concept of Quintessence is typical of the contemporaneous views on the core characteristics of matters. The modernity that stimulates the film is equally anti-transcendentalist and anti-essentialist. Thus, the fifth element of the film is existentially personified and genderized making the traditional philosophical significance of the term to be adjusted by modernity in an immanent and temporal context where in addition aesthetics plays a crucial role. (shrink)

A mistery unveiled, among magic, alchemy and philosophy.

In his book “Galileo’s Error”, Philip Goff lays out what he calls “foundations for a new science of consciousness”, which are decidedly anti-physicalist (panpsychist), motivated by a critique of Galileo’s distinction into knowable objective and unknowable subjective properties and Arthur Eddington’s argument for the limitation of purely structural (physical) knowledge. Here we outline an alternative theory, premised on the Interface Theory of Perception, that too subscribes to a “post-Galilean” research programme. However, interface theorists disagree along several lines. 1. (...) They note that Galileo’s distinction should be replaced by a truly non-dual account, referring to a difference of degree only. 2. They highly appreciate the role of mathematics, in particular when it comes to actually engage scientifically with consciousness. Some notable features of the interface theory are its skepticism towards our epistemic capacities and its rejection of the existence of a public, mind-independent reality. In addition, some interface theorists further employ a thin concept of “conscious agency” to ground their theory. The interface theory leaves open many of the problems of consciousness science (e.g. what is a “self”?) as questions for further (scientific, mathematical) research. (shrink)

Do the same epistemic standards govern scientific and religious belief? Or should science and religion operate in completely independent epistemic spheres? Commentators have recently been divided on William James’s answer to this question. One side depicts “The Will to Believe” as offering a separate-spheres defense of religious belief in the manner of Galileo. The other contends that “The Will to Believe” seeks to loosen the usual epistemic standards so that religious and scientific beliefs can both be justified by a (...) unitary set of evidentiary rules. I argue that James did build a unitary epistemology but not by loosening cognitive standards. In his psychological research, he had adopted the Comtian view that hypotheses and regulative assumptions play a crucial role in the context of discovery even though they must be provisionally adopted before they can be supported by evidence. “The Will to Believe” relies on this methodological point to achieve a therapeutic goal—to convince despairing Victorians that religious faith can be reconciled with a scientific epistemology. James argues that the prospective theist is in the same epistemic situation with respect to the “religious hypothesis” as the scientist working in the context of discovery. (shrink)

Scholarly attempts to analyze the history of science sometime suffer from an imprecise use of terms. In order to understand accurately how science has developed and from where it draws its roots, researchers should be careful to recognize that epistemic regimes change over time and acceptable forms of knowledge production are contingent upon the hegemonic discourse informing the epistemic regime of any given period. In order to understand the importance of this point, I apply the techniques of historical epistemology to (...) an analysis of the place of the study of astrology in the medieval and early modern periods alongside a discussion of the “language games” of these period as well as the role of the “archeology of knowledge” in uncovering meaning in our study of the past. In sum, I argue that the term “science” should never be used when studying approaches to knowledge formation prior to the seventeenth century. (shrink)

For centuries the case of Galileo Galilei has been the cornerstone of every major argument against the church and its supposedly unscientific dogmatism. The church seems to have condemned Galileo for his heresies, just because it couldn’t and wouldn’t handle the truth. Galileo was a hero of science wrongfully accused and now – at last – everyone knows that. But is that true? This paper tries to examine the case from the point of modern physics and the (...) conclusions drawn are startling. It seems that contemporary church was too haste into condemning itself. The evidence provided by Galileo to support the heliocentric system do not even pass simple scrutiny, while modern physics has ruled for a long time now against both heliocentric and geocentric models as depictions of the “truth”. As Einstein eloquently said, the debate about which system is chosen is void of any meaning from a physics’ point of view. At the end, the selection of the center is more a matter of choice rather than a matter of ‘truth’ of any kind. And this choice is driven by specific philosophical axioms penetrating astronomy for hundreds of years now. From Galileo to Hubble, the Copernican principle has been slowly transformed to a dogma followed by all mainstream astronomers. It is time to challenge our dogmatic adherence to the anti-humanism idea that we are insignificant in the cosmos and start making true honest science again, as Copernicus once postulated. (shrink)

Throughout her philosophical writing, Margaret Cavendish is clear in stating that colours are real; they are not mere mind-dependent qualities that exist only in the mind of perceivers. This puts her at odds with other seventeenthcentury thinkers such as Galileo and Descartes who endorsed what would come to be known as the ‘primary-secondary quality distinction’. Cavendish’s argument for this view is premised on two claims. First, that colourless objects are inconceivable. Second, that if an object is inconceivable then it (...) could not possibly exist in nature. My aim in this paper is to explain why Cavendish accepts both premises of this argument. However, the repercussions of this paper go much further than just explaining why she thinks colourless objects cannot exist in nature and the upshots are twofold. First, it provides new insights into the fundamental role that perception plays in Cavendish’s metaphysics. While Cavendish’s view that all of nature perceives is well-established, I show that Cavendish is also committed to the view that all of nature is perceivable. Second, it provides the first in-depth discussion of Cavendish’s modal epistemology and her reasons for thinking that inconceivability entails impossibility (in nature). (shrink)

I argue that Galileo regarded unaccelerated motion as requiring cause to sustain in. In an inclined plane experiment, the cause ceases when the incline ceases. When the incline ceases, what ceases is acceleration, not motion. Hence, unaccelerated motion requires no cause to sustain it.

Galileo proposed what has been called a proto-inertial principle, according to which a body un horizontal motion will conserve its motion. This statement is only true in counterfactual circumstances where no impediments are present. This paper analyzes how Galileo could have been justified in ascribing definite properties to this idealized motion. This analysis is then used to better understand the relation of Galileo’s proto-inertial principle to the classical inertial principle.

Galileo asked in his Dialogue of the Two New Sciences what relationship exists between the size of the set of all natural numbers and the size of the set of all square natural numbers. Although one is a proper subset of the other, suggesting that there are strictly fewer squares than natural numbers, the existence of a simple one-to-one correspondence between the two sets suggests that they have, in fact, the same size. Cantor famously based the modern notion of (...) cardinality on the second intuition, but recent advances in mathematical logic (most notably, numerosity theory) have renewed an interest in the question whether Cantor’s way out of Galileo’s paradox was the only possible one. I present a new solution to Galileo’s paradox and argue that it is a better alternative to the Cantorian solution than numerosity theory. In fact, I argue that it is the best possible way out of Galileo's Paradox that can be based on the "Euclidean" intuition that the whole is always greater than any of its proper parts. (shrink)

How Galileo Galilei discovered the law of fall, and the difference that this makes Galileo’s law of fall is one of the crucial building blocks of classical mechanics. The question how this law was discovered has often been a topic of debate. This article offers a reconstruction of the developments within Galileo’s research that led to the discovery of the law. This reconstruction is offered to make a philosophical point regarding the epistemic status of experimental results: (...) class='Hi'>Galileo’s experiments can offer sufficient justification for the acceptance of the law of fall only because of their place in a broad research programme. (shrink)

The seventeenth century was an important period in the conceptual development of the notion of the infinite. In 1643, Evangelista Torricelli (1608-1647)—Galileo’s successor in the chair of mathematics in Florence—communicated his proof of a solid of infinite length but finite volume. Many of the leading metaphysicians of the time, notably Spinoza and Leibniz, came out in defense of actual infinity, rejecting the Aristotelian ban on it, which had been almost universally accepted for two millennia. Though it would be another (...) two centuries before the notion of the actually infinite was rehabilitated in mathematics by Dedekind and Cantor (Cauchy and Weierstrass still considered it mere paradox), their impenitent advocacy of the concept had significant reverberations in both philosophy and mathematics. In this essay, I will attempt to clarify one thread in the development of the notion of the infinite. In the first part, I study Spinoza’s discussion and endorsement, in the Letter on the Infinite (Ep. 12), of Hasdai Crescas’ (c. 1340-1410/11) crucial amendment to a traditional proof of the existence of God (“the cosmological proof” ), in which he insightfully points out that the proof does not require the Aristotelian ban on actual infinity. In the second and last part, I examine the claim, advanced by Crescas and Spinoza, that God has infinitely many attributes, and explore the reasoning that motivated both philosophers to make such a claim. Similarities between Spinoza and Crescas, which suggest the latter’s influence on the former, can be discerned in several other important issues, such as necessitarianism, the view that we are compelled to assert or reject a belief by its representational content, the enigmatic notion of amor Dei intellectualis, and the view of punishment as a natural consequent of sin. Here, I will restrict myself to the issue of the infinite, clearly a substantial topic in itself. (shrink)

The essays gathered in this issue of the journal Noctua focus on the various relationships that were established between philosophy and mathematics from Galileo and Descartes to Kant, passing by Newton.

The notion of space is one of the most discussed within classical physics concepts. The works of Copernicus and Galileo, as well as Gassendi´s ideas led to Newton to regard it as substance. This conception of space, allows the notion of symmetry is present in an indirect or implied, within the laws of physics, formed through the notions of equivalence and balance. The aim of this study is to identify the symmetry, through such notions, under the study of indistinction (...) between the repose state and the state of uniform translational movement known as the law of inertia. The philosophical approach is framed in the link between these notions and the problem of indistinguishability between states of different movement. We will discuss first the conception of space Telesio and Gassendi that led Newton to his absolutist conception of space. The conception of space and its relationship with Newton symmetry is the second part of our work. As a third part present linking of the Newtonian space with notions of balance, symmetry and equivalence. Subsequently they give our conclusions. (shrink)

The legacy of the Platonic dialogues may well lie, not in any classical idealist “doctrine of forms,” but in an inquisitive stance towards the puzzle behind any such doctrine—how thought can be about anything at all. This Platonic puzzle may, however, yield a different guise of idealism that is recognizably diagnostic: it aims to dispel our worry about thought’s objectivity as a confusion, engendered by a self-alienation of thought. These themes of diagnosis and idealism resurface in Wittgenstein, who in his (...) treatment of rules calls for an understanding of thought’s normativity from within. This is taken up by Cora Diamond, who urges philosophy to attend to thought’s real needs by exorcizing any desire for agreement with something other than itself. I argue that Wittgenstein and Diamond lead us back to Kant’s idealism, which identifies transcendental realism as the deep-seated prejudice at the root of the puzzle. (shrink)

The hard problem – focusing essentially on vision here – is in fact the problem of the origin of our image of the external world. This formulation in terms of the “image” is never seen stated, for the forms populating our image of the world are considered computable, and not considered qualia – the “redness” of the cube is the problem, not the cube as form. Form, however, cannot be divorced from motion and hence from time. Therefore we must examine (...) the classical, spatial metaphysic of space and time, for practical purposes initiated by Galileo, wherein the real has been equated with the quantitative and wherein quality has been stripped from the material world. In this metaphysic, which sees form as quantitative or computable, the origin of qualia is problematic, with a problem of even greater primacy becoming the “memory” that supports the transforming events of perception, e.g., rotating cubes, buzzing flies, twisting leaves. It is this memory, supporting time-extended, flowing events, that necessarily supports all qualia. The concept of storage of “snapshots” of time-flowing events, a notion which the classic metaphysic engenders, is unworkable as a solution to the perception of these flows. Form, in fact being dynamic and defined over flowing fields, equally is a quality, equally requires this memory, and since forms populate the image, the origin of the entire image is indeed a problem. The counter-proposal becomes Bergson’s temporal metaphysic wherein motion is indivisible (or non-differentiable), the global motion of the universal field itself then carrying an intrinsic form of memory. In this framework, with this field viewed as holographic, Bergson provides a unique solution – one that leaves the problem of representation behind – as to how the brain specifies the qualitative image of the dynamically transforming external world. (shrink)

Michiel Wielema: The March of the Libertines. Spinozists and the Dutch Reformed Church (1660–1750). ReLiC: Studies in Dutch Religious History. Hilversum: Uitgeverij Verloren, 2004; pp. 221. The Dutch Republic of the seventeenth century is famous for having cultivated an extraordinary climate of toleration and religious pluralism — the Union of Utrecht supported religious freedom, or “freedom of conscience”, and expressly forbade reli- gious inquisition. However, despite membership in the state sponsored Calvinist Dutch Reformed Church not being compulsory, the freedom (...) to gather and worship, or “to air anti-Christian or atheistic opinions” was little tolerated “within” the organized structure of the church, which functioned more as “an exclusive organisation for those willing to submit freely to certain confessional canons and to the disciplinary author- ity of the church’s governing bodies” (10): the consistories, classes, and synods. Those not prepared to submit to Reformed doctrine were free to leave the church without fear of any legal or political repercussions. However, for those not prepared to leave for reasons of personal belief, matters turned out to be quite different. Because the Reformed Church enjoyed full State protection, matters of doctrinal conflict could well evolve into political affairs. And, contrary to the Union of Utrecht, religious inquisition was in some cases actually applied with political approval for “heretics” within the Reformed Church. The main focus of The March of the Libertines is an investigation of this obvious tension. (shrink)

This article presents an analysis of the bust of Galileo that Vincenzo Vela created for his house and studio at Ligornetto. The work carries symbolic significance in that it was conceived by the Ticinese artist for the pilaster on the right hand side of the principal entrance to the villa, as a counterpart to the bust of Christopher Columbus on the left. It thus served to perpetuate a long-standing literary topos which started at the beginning of the 17th century (...) and which was made use of during the Risorgimento to celebrate Italian ascendency within a European context. Through this work Vela reveals his adherence to patriotic ideals that he had previously expressed through his active participation in the first Italian War of Independence, fighting in the anti-Austrian ranks. (shrink)

This paper will analyze three historical cases (Francis Bacon, Galileo Galilei and Margaret Cavendish) that exemplify the complexity of the interaction between science and religion in the Scientific Revolution and confirm the interpretation of J. H. Brooke, according to which, in this historical context –rather than a separation- a differentiation took hold between them. We will hold that although these authors agreed in proposing the separation of science and religion as an ideal, each in their own way made an (...) articulation between the two that in the long run prevented a complete separation. This articulation was due to both epistemic and extra-epistemic reasons and manifests a tension that was characteristic of the Scientific Revolution. (shrink)

In his 1615 letter to the Grand Duchess Christina of Lorraine, Galileo argues for a “principle of limitation”: the authority of Scripture should not be invoked in scientific matters. In doing so, he claims to be following the example of St Augustine. But Augustine’s position would be better described as a “principle of differing purpose”: although the Scriptures were not written in order to reveal scientific truths, such matters may still be covered by biblical authority. The Roman Catholic Church (...) has rejected Galileo’s principle, opting rather for Augustine’s, leaving open the possibility of future conflicts between scientists and Church authority. (shrink)