On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic and causal. We also establish the (...) consistency of our axioms and discuss the philosophical implications. (shrink)

In [16], Peterzil and Steinhorn proved that if a group G definable in an o-minimal structure is not definably compact, then G contains a definable torsion-free subgroup of dimension 1. We prove here a p-adic analogue of the Peterzil–Steinhorn theorem, in the special case of abelian groups. Let G be an abelian group definable in a p-adically closed field M. If G is not definably compact then there is a definable subgroup H of dimension 1 which is not (...) definably compact. In a future paper we will generalize this to non-abelian G. (shrink)

The two theories that revolutionized physics in the twentieth century, relativity and quantum mechanics, are full of predictions that defy common sense. Recently, we used three such paradoxical ideas to prove “The Free Will Theorem” (strengthened here), which is the culmination of a series of theorems about quantum mechanics that began in the 1960s. It asserts, roughly, that if indeed we humans have free will, then elementary particles already have their own small share of this (...) valuable commodity. More precisely, if the experimenter can freely choose the directions in which to orient his apparatus in a certain measurement, then the particle’s response (to be pedantic—the universe’s response near the particle) is not determined by the entire previous history of the universe. Our argument combines the well-known consequence of relativity theory, that the time order of space-like separated events is not absolute, with the EPR paradox discovered by Einstein, Podolsky, and Rosen in 1935, and the Kochen-Specker Paradox of 1967 (See [2].) We follow Bohm in using a spin version of EPR and Peres in using his set of 33 directions, rather than the original configuration used by Kochen and Specker. More contentiously, the argument also involves the notion of free will, but we postpone further discussion of this to the last section of the article. Note that our proof does not mention “probabilities” or the “states” that determine them, which is.. (shrink)

Conway and Kochen have presented a “free will theorem” [4, 6] which they claim shows that “if indeed we humans have free will, then [so do] elementary particles.” In a more precise fashion, they claim it shows that for certain quantum experiments in which the experimenters can choose between several options, no deterministic or stochastic model can account for the observed outcomes without violating a condition “MIN” motivated by relativistic symmetry. We point out that for (...) stochastic models this conclusion is not correct, while for deterministic models it is not new. In the way the free will theorem is formulated and proved, it only concerns deterministic models. But Conway and Kochen have argued [4, 5, 6, 7] that “randomness can’t help,” meaning that stochastic models are excluded as well if we insist on the conditions “SPIN”, “TWIN”, and “MIN”. We point out a mistake in their argument. Namely, the theorem is of the form deterministic model with SPIN & TWIN & MIN ⇒ contradiction , (1) and in order to derive the further claim, which is of the form stochastic model with SPIN & TWIN & MIN ⇒ contradiction , (2) Conway and Kochen propose a method for converting any stochastic model into a deterministic one [4]. (shrink)

In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber (RW) type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys. 115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.

If the concept of “free will” is reduced to that of “choice” all physical world share the latter quality. Anyway the “free will” can be distinguished from the “choice”: The “free will” involves implicitly certain preliminary goal, and the choice is only the mean, by which it can be achieved or not by the one who determines the goal. Thus, for example, an electron has always a choice but not free will unlike (...) a human possessing both. Consequently, and paradoxically, the determinism of classical physics is more subjective and more anthropomorphic than the indeterminism of quantum mechanics for the former presupposes certain deterministic goal implicitly following the model of human freewill behavior. The choice is usually linked to very complicated systems such as human brain or society and even often associated with consciousness. In its background, the material world is deterministic and absolutely devoid of choice. However, quantum mechanics introduces the choice in the fundament of physical world, in the only way, in which it can exist: All exists in the “phase transition” of the present between the uncertain future and the well-ordered past. Thus the present is forced to choose in order to be able to transform the coherent state of future into the well-ordering of past. The concept of choice as if suggests that there is one who chooses. However quantum mechanics involves a generalized case of choice, which can be called “subjectless”: There is certain choice, which originates from the transition of the future into the past. Thus that kind of choice is shared of all existing and does not need any subject: It can be considered as a low of nature. There are a few theorems in quantum mechanics directly relevant to the topic: two of them are called “free will theorems” by their authors, Conway and Kochen, and according to them: “Do we really have free will, or, as a few determined folk maintain, is it all an illusion? We don’t know, but will prove in this paper that if indeed there exist any experimenters with a modicum of free will, then elementary particles must have their own share of this valuable commodity” “The import of the free will theorem is that it is not only current quantum theory, but the world itself that is non-deterministic, so that no future theory can return us to a clockwork universe”. Those theorems can be considered as a continuation of the so-called theorems about the absence of “hidden variables” in quantum mechanics. (shrink)

One has it that earlier circumstances and the laws of nature uniquely determine later circumstances, and the other has it that past present and future all exist tenselessly in a ‘block universe,’ so that the passage of time and associated changes in the world are illusions or at best merely apparent.

We respond to criticisms of our paper “The Free Will Theorem”, and produce a new form of the theorem based on weaker assumptions.

We review the argument that latent image formation is a measurement in which the state vector collapses, requiring an enhanced noise parameter in objective reduction models. Tentative observation of a residual noise at this level, plus several experimental bounds, imply that the noise must be colored, and hence frame dependent and non-relativistic. Thus a relativistic objective reduction model, even if achievable in principle, would be incompatible with experiment; the best one can do is the non-relativistic CSL model. This negative conclusion (...) has a positive aspect, in that the non-relativistic CSL reduction model evades the argument leading to the Conway–Kochen “Free Will Theorem”. (shrink)

The determinism-free will debate is perhaps as old as philosophy itself and has been engaged in from a great variety of points of view including those of scientific, theological, and logical character. This chapter focuses on two arguments from logic. First, there is an argument in support of determinism that dates back to Aristotle, if not farther. It rests on acceptance of the Law of Excluded Middle, according to which every proposition is either true or false, no matter (...) whether the proposition is about the past, present or future. In particular, the argument goes, whatever one does or does not do in the future is determined in the present by the truth or falsity of the corresponding proposition. The second argument coming from logic is much more modern and appeals to Gödel's incompleteness theorems to make the case against determinism and in favour of free will, insofar as that applies to the mathematical potentialities of human beings. The claim more precisely is that as a consequence of the incompleteness theorems, those potentialities cannot be exactly circumscribed by the output of any computing machine even allowing unlimited time and space for its work. The chapter concludes with some new considerations that may be in favour of a partial mechanist account of the mathematical mind. (shrink)

In this paper, I argue that Conway and Kochen’s Free Will Theorem (1,2) to the conclusion that quantum mechanics and relativity entail freedom for the particles, does not change the situation in favor of a libertarian position as they would like. In fact, the theorem more or less implicitly assumes that people are free, and thus it begs the question. Moreover, it does not prove neither that if people are free, so are particles, nor (...) that the property people possess when they are said to be free is the same as the one particles possess when they are claimed to be free. I then analyze the Free State Theorem (2), which generalizes the Free Will Theorem without the assumption that people are free, and I show that it does not prove anything about free will, since the notion of freedom for particles is either inconsistent, or it does not concern our common understanding of freedom. In both cases, the Free Will Theorem and the Free State Theorem do not provide any enlightenment on the constraints physics can pose on free will. (shrink)

If the concept of “free will” is reduced to that of “choice” all physical world shares the latter quality. Anyway the “free will” can be distinguished from the “choice”: The “free will” involves implicitly a certain goal, and the choice is only the mean, by which the aim can be achieved or not by the one who determines the target. Thus, for example, an electron has always a choice but not free will (...) unlike a human possessing both. Consequently, and paradoxically, the determinism of classical physics is more subjective and more anthropomorphic than the indeterminism of quantum mechanics for the former presupposes certain deterministic goal implicitly following the model of human freewill behavior. Quantum mechanics introduces the choice in the fundament of physical world involving a generalized case of choice, which can be called “subjectless”: There is certain choice, which originates from the transition of the future into the past. Thus that kind of choice is shared of all existing and does not need any subject: It can be considered as a low of nature. There are a few theorems in quantum mechanics directly relevant to the topic: two of them are called “free will theorems” by their authors (Conway and Kochen 2006; 2009). Any quantum system either a human or an electron or whatever else has always a choice: Its behavior is not predetermined by its past. This is a physical law. It implies that a form of information, the quantum information underlies all existing for the unit of the quantity of information is an elementary choice: either a bit or a quantum bit (qubit). (shrink)

Do humans have a free choice of which actions to perform? Three recent developments of modern science can help us to answer this question. First, new investigative tools have enabled us to study the processes in our brains which accompanying our decisions. The pioneer work of Benjamin Libet has led many neuroscientists to hold the view that our conscious intentions do not cause our bodily movements but merely accompany them. Then, Quantum Theory suggests that not all physical events are (...) fully determined by their causes, and so opens the possibility that not all brain events may be fully determined by their causes, and so maybe - if neuroscience does not rule this out - there is a role for intentions after all. Finally, a theorem of mathematics, Godel's theory, has been interpreted to suggest that the initial conditions and laws of development of a mathematician's brain could not fully determine which mathematical conjectures he sees to be true. Papers by Patrick Haggard, Tim Bayne, Harald Atmanspacher and Stefan Rotter, Solomon Feferman, and John Lucas investigate these issues. The extent to which human behaviour is determined by brain events may well depend on whether conscious events, such as intentions, are themselves merely brain events, or whether they are separate events which interact with brain events (perhaps in the radical form that intentions are events in our soul, and not in our body). The papers of Frank Jackson, Richard Swinburne, and Howard Robinson investigate these issues. The remaining papers, of Galen Strawson, Helen Steward, and R.A. Duff, consider what kind of free will we need in order to be morally responsible for our actions or to be held guilty in a court of law. Is it sufficient merely that our actions are uncaused by brain events, or what? (shrink)

In physics, free will is debated mainly in regard to the observer-dependent effects. To eliminate them from quantum mechanics, superdeterminism postulates that the universe is a computation, and consciousness is an automaton. As a result, free will is impossible. Quantum no-go theorems tell us that the only natural phenomenon that might be able to account for every bit of freedom in the universe is quantum randomness. With randomness in Nature, the universe could not have been predetermined (...) completely in the sense that it should be impossible in principle to compute from the big bang or at any later moment whether live and conscious observers might or might not appear there. After all, superdeterminism comes to be either self-inconsistent by assuming randomness, at least, at the initial conditions of the big bang, or untestable and mysterious by pushing every bit of freedom in back to the prerequisites of the universe “designed” in the big bang. (shrink)

I wish to discuss a large, interwoven set of topics pointed at in the title above. Much of what I say is highly speculative, some is testable, some is, at present, surely not. It is, I hope, useful, to set these ideas forth for our consideration. What I shall say assumes quantum measurement is real, and that Bohm's interpretation of Quantum Mechanics is not true. The Stalemate: In our contemporary neurobiology and much of the philosophy of mind post Descartes we (...) are classical physics machines and either mindless, or mind is at best epiphenomenal and can have no consequences for the physical world. The first main point of this paper is that we are not forced to this conclusion, but must give up total reliance on classical physics. Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}. (shrink)

Four studies measured or manipulated beliefs in free will to illuminate how such beliefs are linked to other aspects of personality. Study 1 showed that stronger belief in free will was correlated with more gratitude, greater life satisfaction, lower levels of perceived life stress, a greater sense of self-efficacy, greater perceived meaning in life, higher commitment in relationships, and more willingness to forgive relationship partners. Study 2 showed that the belief in free will was (...) a stronger predictor of life satisfaction, meaning in life, gratitude, and self-efficacy than either locus of control or implicit person theory. Study 3 showed that experimentally manipulating disbelief in free will caused a reduction in the perceived meaningfulness of life. Study 4 found that inducing a stronger belief in free will caused people to set more meaningful goals for themselves. The possible concern that believers in free will simply claim all manner of positive traits was contradicted by predicted null finding.. (shrink)

in a very different sense, to refer to the cultural community, or cultural structure, itself On this view, the cultural community continues to exist even when its members arc free to modify the character of the culture, should they find its traditional ...

The aim of UK-REACH (“The United Kingdom Research study into Ethnicity And COVID-19 outcomes in Healthcare workers”) is to understand if, how, and why healthcare workers (HCWs) in the United Kingdom (UK) from ethnic minority groups are at increased risk of poor outcomes from COVID-19. In this article, we present findings from the ethical and legal stream of the study, which undertook qualitative research seeking to understand and address legal, ethical, and social acceptability issues around data protection, privacy, and information (...) governance associated with the linkage of HCWs’ registration data and healthcare data. We interviewed 22 key opinion leaders in healthcare and health research from across the UK in two-to-one semi-structured interviews. Transcripts were coded using qualitative thematic analysis. Participants told us that a significant aspect of Big Data research in public health is varying drivers of mistrust—of the research itself, research staff and funders, and broader concerns of mistrust within participant communities, particularly in the context of COVID-19 and those situated in more marginalised community settings. However, despite the challenges, participants also identified ways in which legally compliant and ethically informed approaches to research can be crafted to mitigate or overcome mistrust and establish greater confidence in Big Data public health research. Overall, our research indicates that a “Big Data Ethics by Design” approach to research in this area can help assure (1) that meaningful community and participant engagement is taking place and that extant challenges are addressed, and (2) that any new challenges or hitherto unknown unknowns can be rapidly and properly considered to ensure potential (but material) harms are identified and minimised where necessary. Our findings indicate such an approach, in turn, will help drive better scientific breakthroughs that translate into medical innovations and effective public health interventions, which benefit the publics studied, including those who are often marginalised in research. (shrink)

In recent years, model theory has widened its scope to include metric structures by considering real-valued models whose underlying set is a complete metric space. We show that it is possible to carry out this work by giving presentation theorems that translate the two main frameworks into discrete settings. We also translate various notions of classification theory.

Is a logicist bound to the claim that as a matter of analytic truth there is an actual infinity of objects? If Hume’s Principle is analytic then in the standard setting the answer appears to be yes. Hodes’s work pointed to a way out by offering a modal picture in which only a potential infinity was posited. However, this project was abandoned due to apparent failures of cross-world predication. We re-explore this idea and discover that in the setting of the (...) potential infinite one can interpret first-order Peano arithmetic, but not second-order Peano arithmetic. We conclude that in order for the logicist to weaken the metaphysically loaded claim of necessary actual infinities, they must also weaken the mathematics they recover. (shrink)

We combine two notions in AECs, tameness and good λ-frames, and show that they together give a very well-behaved nonforking notion in all cardinalities. This helps to fill a longstanding gap in classification theory of tame AECs and increases the applicability of frames. Along the way, we prove a complete stability transfer theorem and uniqueness of limit models in these AECs.

Our conscious minds exist in the Universe, therefore they should be identified with physical states that are subject to physical laws. In classical theories of mind, the mental states are identified with brain states that satisfy the deterministic laws of classical mechanics. This approach, however, leads to insurmountable paradoxes such as epiphenomenal minds and illusionary free will. Alternatively, one may identify mental states with quantum states realized within the brain and try to resolve the above paradoxes using the (...) standard Hilbert space formalism of quantum mechanics. In this essay, we first show that identification of mind states with quantum states within the brain is biologically feasible, and then elaborating on the mathematical proofs of two quantum mechanical no-go theorems, we explain why quantum theory might have profound implications for the scientific understanding of one's mental states, self identity, beliefs and free will. (shrink)

IN THIS PAPER I ATTEMPT TO UNDERSTAND HEGEL’S CLAIM that the moral will is finite, or incompletely free, as a consequence of the moral will being structured by the logical concept of judgment. Section 2 begins with a brief discussion of judgment. It then identifies the defining features of the moral will and compares them to those of judgment, enabling us to conclude that judgment is the logical structure of the moral will. Section 3 considers (...) the limitations that plague judgment and produce the finitude of the moral will. Section 4 examines three separate attempts of the moral will to overcome this finitude, all of which fail in virtue of their own logical structures. This allows us to conclude that the moral will is insuperably finite, and that the will must be reconceived as having a different logical structure in ethical life if it is to be free. (shrink)

IN THIS PAPER I ATTEMPT TO UNDERSTAND HEGEL’S CLAIM that the moral will is finite, or incompletely free, as a consequence of the moral will being structured by the logical concept of judgment. Section 2 begins with a brief discussion of judgment. It then identifies the defining features of the moral will and compares them to those of judgment, enabling us to conclude that judgment is the logical structure of the moral will. Section 3 considers (...) the limitations that plague judgment and produce the finitude of the moral will. Section 4 examines three separate attempts of the moral will to overcome this finitude, all of which fail in virtue of their own logical structures. This allows us to conclude that the moral will is insuperably finite, and that the will must be reconceived as having a different logical structure in ethical life if it is to be free. (shrink)

Let us recall that Raphael Robinson's Arithmetic Q is an axiom system that differs from Peano Arithmetic essentially by containing no Induction axioms [13], [18]. We will generalize the semantic-tableaux version of the Second Incompleteness Theorem almost to the level of System Q. We will prove that there exists a single rather long Π 1 sentence, valid in the standard model of the Natural Numbers and denoted as V, such that if α is any finite consistent extension (...) of Q + V then α will be unable to prove its Semantic Tableaux consistency. The same result will also apply to axiom systems α with infinite cardinality when these infinite-sized axiom systems satisfy a minor additional constraint, called the Conventional Encoding Property. Our formalism will also imply that the semantic-tableaux version of the Second Incompleteness Theorem generalizes for the axiom system IΣ 0 , as well as for all its natural extensions. (This answers an open question raised twenty years ago by Paris and Wilkie [15].). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Hegel’s Theory of Self-Conscious Life by Guido SeddoneWill DesmondSEDDONE, Guido. Hegel’s Theory of Self-Conscious Life. Leiden: Brill, 2023. 155 pp. Cloth, $138.00Guido Seddone’s monograph explores an ensemble of issues centering on what he terms Hegelian “naturalism.” He argues that “Hegel’s philosophy represents a novel version of naturalism since it stresses the mutual dependence between nature and spirit, rather than just conceiving of spirit as a substance emerging and (...) separating from bodily natural requisites.” Seddone avoids scholarly exegeses to address instead “theoretical and systematic aspects of the Hegelian philosophy.” He focusses on “life” and “self-consciousness” as the conceptual keys to those parts of Hegel that remain compelling for relevant contemporary debates. “This book is, therefore, based on the dialogue between Hegel [End Page 361] and contemporary thinkers and strives to enhance our understanding of theoretical and practical issues and to widen the grammar of the philosophical thought.” The book’s chapters proceed from the more abstract to the more concrete—essentially from issues of logic, epistemology, and psychology to morality, society, and history.Chapter 1 (“Science of Logic: The Logical Premises of Hegel’s Naturalism”) argues that the categories of “Teleology” and “Life” in Hegel’s Science of Logic mark the critical transition in his naturalism from the sciences of physics (“Mechanism”) and chemistry (“Chemism”) to biology, as well as from external nature to inner self-consciousness and cognition. Seddone helpfully points to Hegel’s revisions of Kant’s subordination of teleological language (merely heuristic) to mechanical explanation. Most promising is the comparison of the “self-referring negativity” of Hegelian “life” to discussions by Evan Thompson and Francisco Varela of the cell—whose permeable membrane enables it to be more than its merely chemical environment.Chapter 2 (“Self-Consciousness”) takes a rather bird’s-eye approach to the Phenomenology of Spirit, offering a basic reading of Hegelian self-consciousness and Geist in relation to the Cartesian cogito and Kantian unity of apperception. Scattered remarks about animal desire and the master–slave relation could be clarified to better explore a naturalistic basis of the Hegelian conception of mind. One is struck by the dearth of specific texts from the section “Self-Consciousness”: Seddone seems content with some well-known quotations (for example, Geist as an “I that is We and We that is I”) punctuating large generalizations.Chapter 3 does not quite live up to its title (“The Hegelian Theory about the (Human) Biological Organism”) in that it focuses primarily on Hegel’s “treatise about habits” in the Encyclopaedia of the Philosophical Sciences. Here habit is construed as a second nature, and hence a further step toward self-conscious, relational mind: Habits are “universal ways of the soul, i.e. ways in which individual soul [sic] incorporates feelings by evolving general rules and practices.”The last section of chapter 4 (“Extended and Embodied Mind”) reverts to habits as moments of the feeling soul but dissociates Hegel’s notion of Verleiblichung from contemporary discussions of embodied mind. By contrast, Seddone argues for retranslating Hegelian Geist as “common mind” and juxtaposes this with the related concept of mind (in, for example, Philip Pettit) as “extended” through social entities, with the result that Hegel’s approach is praised as “the state-of-the-art of this topic.”Chapter 5 (“Natural and Self-conscious Agency”) is perhaps the clearest chapter as it presents the dialectic of the abstractly universal will in the initial sections of Philosophy of Right, links this and the Hegelian conception of free agency to his logical category of “actuality,” and proceeds to an illuminating contrast of the Hobbesian and Hegelian visions of society and state. [End Page 362]In tackling attempts to reconcile “Normativity and Freedom,” chapter 6 spends over six pages rehearsing the basics of Kantian autonomy before turning to Hegel’s Phenomenology of Spirit, specifically the master–slave dialectic (again) as the critical moment in the evolution of social norms. “My thesis is that self-conscious life needs recognition in order to achieve the higher form of independence created by social acknowledgement and justification, what [sic] fosters the condition for an authoritative reason that can be socially... (shrink)

"Understanding German Idealism" provides an accessible introduction to the philosophical movement that emerged in 1781, with the publication of Kant's monumental "Critique of Pure Reason", and ended fifty years later, with Hegel's death. The thinkers of this period, and the themes they developed revolutionized almost every area of philosophy and had an impact that continues to be felt across the humanities and social sciences today. Notoriously complex, the central texts of German Idealism have confounded the most capable and patient interpreters (...) for more than 200 years. "Understanding German Idealism" aims to convey the significance of this philosophical movement while avoiding its obscurity. Readers are given a clear understanding of the problems that motivated Kant, Fichte, Schelling and Hegel and the solutions that they proposed. Dudley outlines the main ideas of transcendental idealism and explores how the later German Idealists attempted to carry out the Kantian project more rigorously than Kant himself, striving to develop a fully self-critical and rational philosophy, in order to determine the meaning and sustain the possibility of a free and rational modern life. The book examines some of the most important early criticisms of German Idealism and the philosophical alternatives to which they led, including romanticism, Marxism, existentialism, and naturalism. (shrink)

"Understanding German Idealism" provides an accessible introduction to the philosophical movement that emerged in 1781, with the publication of Kant's monumental "Critique of Pure Reason", and ended fifty years later, with Hegel's death. The thinkers of this period, and the themes they developed revolutionized almost every area of philosophy and had an impact that continues to be felt across the humanities and social sciences today. Notoriously complex, the central texts of German Idealism have confounded the most capable and patient interpreters (...) for more than 200 years. "Understanding German Idealism" aims to convey the significance of this philosophical movement while avoiding its obscurity. Readers are given a clear understanding of the problems that motivated Kant, Fichte, Schelling and Hegel and the solutions that they proposed. Dudley outlines the main ideas of transcendental idealism and explores how the later German Idealists attempted to carry out the Kantian project more rigorously than Kant himself, striving to develop a fully self-critical and rational philosophy, in order to determine the meaning and sustain the possibility of a free and rational modern life. The book examines some of the most important early criticisms of German Idealism and the philosophical alternatives to which they led, including romanticism, Marxism, existentialism, and naturalism. (shrink)

Bell’s Theorem from Physics 36:1–28 (1964) and the (Strong) Free Will Theorem of Conway and Kochen from Notices AMS 56:226–232 (2009) both exclude deterministic hidden variable theories (or, in modern parlance, ‘ontological models’) that are compatible with some small fragment of quantum mechanics, admit ‘free’ settings of the archetypal Alice and Bob experiment, and satisfy a locality condition akin to parameter independence. We clarify the relationship between these theorems by giving reformulations of both that exactly (...) pinpoint their resemblance and their differences. Our reformulation imposes determinism in what we see as the only consistent way, in which the ‘ontological state’ initially determines both the settings and the outcome of the experiment. The usual status of the settings as ‘free’ parameters is subsequently recovered from independence assumptions on the pertinent (random) variables. Our reformulation also clarifies the role of the settings in Bell’s later generalization of his theorem to stochastic hidden variable theories. (shrink)

In a recent paper, Conway and Kochen proposed what is now known as the “Free Will theorem” which, among other things, should prove the impossibility of combining GRW models with special relativity, i.e., of formulating relativistically invariant models of spontaneous wavefunction collapse. Since their argument basically amounts to a non-locality proof for any theory aiming at reproducing quantum correlations, and since it was clear since very a long time that any relativistic collapse model must be non-local in (...) some way, we discuss why the theorem of Conway and Kochen does not affect the program of formulating relativistic GRW models. (shrink)

An account of mathematical understanding should account for the differences between theorems whose proofs are “easy” to discover, and those whose proofs are difficult to discover. Though Hilbert seems to have created proof theory with the idea that it would address this kind of “discovermental complexity”, much more attention has been paid to the lengths of proofs, a measure of the difficulty of _verifying_ of a _given_ formal object that it is a proof of a given formula in a given (...) formal system. In this paper we will shift attention back to discovermental complexity, by addressing a “topological” measure of proof complexity recently highlighted by Alessandra Carbone ( 2009 ). Though we will contend that Carbone’s measure fails as a measure of discovermental complexity, it forefronts numerous important formal and epistemological issues that we will discuss, including the structure of proofs and the question of whether impure proofs are systematically simpler than pure proofs. (shrink)

In this chapter I consider various potential challenges to free will from the modern mind sciences. After motivating the importance of considering these challenges, I outline the argument structure for such challenges: they require simultaneously establishing a particular condition for free will and an empirical challenge to that condition. I consider several potential challenges: determinism, naturalism, and epiphenomenalism, and explain why none of these philosophical challenges is bolstered by new discoveries from neuroscience and psychology. I then (...) respond to relevant empirical challenges to the role of consciousness and rationality in action. (shrink)

Free Will & The Tragic Predicament : Making Sense of Williams -/- The discussion in this paper aims to make better sense of free will and moral responsibility by way of making sense of Bernard Williams’ significant and substantial contribution to this subject. Williams’ fundamental objective is to vindicate moral responsibility by way of freeing it from the distortions and misrepresentations imposed on it by “the morality system”. What Williams rejects, in particular, are the efforts of (...) “morality” to further “deepen” or “refine” the notion of the voluntary, with a view to securing “ultimate justice”. It is these aims and aspirations, he argues, that take us to the precipice of scepticism. In Shame and Necessity (1993) Williams advances a vindicatory genealogy that unmasks the “illusions” and “fantasies” of our current ethical ideas as they relate to agency and responsibility. What we are then left with is the task of “recasting our ethical conceptions” . It is here that Williams is especially insistent on the importance and value of historical consciousness and reflection. The role of our reflections about the Greeks and tragedy is precisely to show that in order to move forward, into the future, we need to first look back at where we have come from. The value of these “untimely” observations is that they provide us with alternatives and options that we might otherwise lack. What we discover, when we consider the Greeks, is their commitment to a “pessimism of strength” that rests on rejecting scepticism. It is this two-sided perspective on our ethical predicament that delivers a more truthful account of our human situation, one that will help us discard those illusions and fantasies of "morality" that we are “better off” without. An account of this kind refuses to accept an optimism that insists that any form of responsible ethical life must be one that is immune to the influence of luck and fate. This is the fundamental lesson that we can learn from the ancient Greeks and that Williams seeks to “recover” for us. (shrink)

This paper is concerned with learners who aim to learn patterns in infinite binary sequences: shown longer and longer initial segments of a binary sequence, they either attempt to predict whether the next bit will be a 0 or will be a 1 or they issue forecast probabilities for these events. Several variants of this problem are considered. In each case, a no-free-lunch result of the following form is established: the problem of learning is a formidably difficult (...) one, in that no matter what method is pursued, failure is incomparably more common that success; and difficult choices must be faced in choosing a method of learning, since no approach dominates all others in its range of success. In the simplest case, the comparison of the set of situations in which a method fails and the set of situations in which it succeeds is a matter of cardinality (countable vs. uncountable); in other cases, it is a topological matter (meagre vs. co-meagre) or a hybrid computational-topological matter (effectively meagre vs. effectively co-meagre). (shrink)

An important and engaging book on a key argument in contemporary debates about free will and moral responsibility.

Denialism concerning free will and moral responsibility combines, in its minimal form, the rejection of libertarian free will and the rejection of compatibilism. I will address the more ambitiously “happy” or “optimistic” version of denialism, which also claims that we are better off without belief in free will and moral responsibility, and ought to try to radically reform our moral, social and personal lives without such beliefs. I argue that such denialism involves, for (...) various reasons, a dangerous gamble, which it would be morally irresponsible to follow. I conclude by reflecting upon the implications. (shrink)

Benjamin Libet's empirical challenge to free will has received a great deal of attention and criticism. A standard line of response has emerged that many take to be decisive against Libet's challenge. In the first part of this paper, I will argue that this standard response fails to put the challenge to rest. It fails, in particular, to address a recent follow-up experiment that raises a similar worry about free will (Soon, Brass, Heinze, & Haynes, (...) 2008). In the second part, however, I will argue that we can altogether avoid Libet-style challenges if we adopt a traditional compatibilist account of free will. In the final section, I will briefly explain why there is good and independent reason to think about free will in this way. (shrink)

FREE WILL. The problem of "free will" has generally been interpreted in modern times in terms of the question of whether or not moral freedom and responsibility are compatible with causality and determinism. Philosophers in the empiricist tradition have defended, with remarkable consistency, a compatibilist position on this issue. Moreover, most of the major figures of the empiricist tradition (i.e. Hobbes, Locke, Hume, Mill, Schlick, and Ayer) are understood to have endorsed and contributed to a single, (...) unified strategy on this subject. The position that these philosophers developed reflects, in large measure, the "antimetaphysical" and naturalistic orientation of empiricist philosophy.... -/- . (shrink)

The present note was prompted by Weber’s approach to proving Cantor’s theorem, i.e., the claim that the cardinality of the power set of a set is always greater than that of the set itself. While I do not contest that his proof succeeds, my point is that he neglects the possibility that by similar methods it can be shown also that no non-empty set satisfies Cantor’s theorem. In this paper unrestricted abstraction based on a cut free Gentzen (...) type sequential calculus will be employed to prove both results. In view of the connection between Priest’s three-valued logic of paradox and cut free Gentzen calculi this, a fortiori, has an impact on any paraconsistent set theory built on Priest’s logic of paradox. (shrink)

It is often called “the problem of free will and determinism,” as if the only thing that might challenge free will is determinism and as if determinism is obviously a problem. The traditional debates about free will have proceeded accordingly. Typically, incompatibilists about free will and determinism suggest that their position is intuitive or commonsensical, such that compatibilists have the burden of showing how, despite appearances, the problem of determinism is not really (...) a problem. Compatibilists, in turn, tend to proceed as if showing that determinism is not a problem thereby shows that we have free will, as if determinism is the only thing that might threaten free will. In this chapter, I reject both of these elements of the traditional debate; the question of whether we have free will should neither begin nor end with the so-called problem of determinism. I present and discuss evidence from a variety of studies that suggests that incompatibilism is not particularly intuitive. Most people do not have to be talked out of incompatibilism but rather talked into it. This provides some reasons—though certainly not decisive reasons—to think that compatibilism is true. I conclude by pointing out that, even if compatibilism were true, it would not dissolve the problem of free will, because there are problems other than determinism that need to be confronted—namely, challenges to free will suggested by current and “future science,” including neuroscience and psychology. The threats to free will suggested by these sciences are distinct from the traditional threat of determinism, and they are the ones that “ordinary persons” find intuitively threatening to free will. In fact, I will argue that the reason incompatibilism about free will and determinism appears to be intuitive is that determinism is often and easily misunderstood to involve these distinct threats to free will—threats that suggest that our rational, conscious mental activity is bypassed in the process of our making decisions and coming to act. (shrink)

This article examines the free will problem as it arises within Thomas Hobbes' naturalistic science of morals in early modern Europe. It explains that during this period, the problem of moral and legal responsibility became acute as mechanical philosophy was extended to human psychology and as a result human choices were explained in terms of desires and preferences rather than being represented as acts of an autonomous faculty. It describes how Hobbes changed the face of moral philosophy, through (...) his Leviathan, in ways that still structure and resonate within the contemporary debate. (shrink)

A Gedanken experiment is presented where an excited and a ground-state atom are positioned such that, within the former’s half-life time, they exchange a photon with 50% probability. A measurement of their energy state will therefore indicate in 50% of the cases that no photon was exchanged. Yet other measurements would reveal that, by the mere possibility of exchange, the two atoms have become entangled. Consequently, the “no exchange” result, apparently precluding entanglement, is non-locally established between the atoms by (...) this very entanglement. This quantum-mechanical version of the ancient Liar Paradox can be realized with already existing transmission schemes, with the addition of Bell’s theorem applied to the no-exchange cases. Under appropriate probabilities, the initially-excited atom, still excited, can be entangled with additional atoms time and again, or alternatively, exert multipartite nonlocal correlations in an interaction free manner. When densely repeated several times, this result also gives rise to the Quantum Zeno effect, again exerted between distant atoms without photon exchange. We discuss these experiments as variants of interaction-free-measurement, now generalized for both spatial and temporal uncertainties. We next employ weak measurements for elucidating the paradox. Interpretational issues are discussed in the conclusion, and a resolution is offered within the Two-State Vector Formalism and its new Heisenberg framework. (shrink)