A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but (...) Howson is speaking of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

Here I respond to Anthony Brueckner and John Martin Fischer’s “The Evil of Death: A Reply to Yi.” They developed an influential strategy in defense of the deprivation account of death’s badness against the Lucretian symmetry problem. The core of their argument consists in the claim that it is rational for us to welcome future intrinsic goods while being indifferent to past intrinsic goods. Previously, I argued that their approach is compatible with the evil of late birth insofar as (...) an earlier birth would have generated more goods in the future. In reply, Brueckner and Fischer argue that my critique fails to appreciate an important aspect of their thought experiment, which aims only to show that the deprivation of past goods per se is not bad for us. Thus, purportedly, my critique poses no threat to their view. Here I argue that since the deprivation account explains the evil of death with recourse to how one’s life would have fared had one lived longer, it ought to respond to the symmetry problem with reference to how one’s life would have fared had one been born earlier. However, it is not generally true that the life one would have had with an earlier birth is not preferable to one’s actual life, because in many cases such a life would contain more future goods. (shrink)

ABSTRACT This article is a response to 'Fear of death and the symmetry argument', in this issue. In that article, the author discusses the above Lucretian symmetry argument, and proposes a view that justifies the existing asymmetry in our attitudes towards birth and death. I begin by distinguishing this symmetry argument from a different one, also loosely inspired by Lucretius, which also plays a role in the article. I then describe what I take to be the author's (...) solution to the original symmetry argument and explain why I am unpersuaded by it. (shrink)

The modal ontological argument (MOA) proceeds from God’s possible existence to God’s actual existence. A prominent objection to the MOA is that it suffers from a symmetry problem: an exactly parallel modal ontological argument can be given for God's non-existence. Several attempts have been made to break the symmetry between the arguments. This draft is a mostly comprehensive survey of those attempts. -/- The draft was initially written as a supplement to the 2024 Summer edition of the (...) SEP entry on Ontological Arguments. However, the draft is not included in the SEP entry. (shrink)

The leaders of the Scientific Revolution were not Baconian in temperament, in trying to build up theories from data. Their project was that same as in Aristotle's Posterior Analytics: they hoped to find necessary principles that would show why the observations must be as they are. Their use of mathematics to do so expanded the Aristotelian project beyond the qualitative methods used by Aristotle and the scholastics. In many cases they succeeded.

Science and mathematics continually change in their tools, methods, and concepts. Many of these changes are not just modifications but progress---steps to be admired. But what constitutes progress? This dissertation addresses one central source of intellectual advancement in both disciplines: reformulating a problem-solving plan into a new, logically compatible one. For short, I call these cases of compatible problem-solving plans "reformulations." Two aspects of reformulations are puzzling. First, reformulating is often unnecessary. Given that we could already solve a problem using (...) an older formulation, what do we gain by reformulating? Second, some reformulations are genuinely trivial or insignificant. Merely replacing one symbol with another does not lead to intellectual progress. What distinguishes significant reformulations from trivial ones? According to what I call "conceptualism" (or "conceptual empiricism"), reformulations are intellectually significant when they provide a different plan for solving problems. Significant reformulations provide inferentially different routes to the same solution. In contrast, trivial reformulations provide exactly the same problem-solving plans, and hence they do not change our understanding. This answers the second question about what distinguishes trivial from significant reformulations. However, the first question remains: what makes a new way of solving an old problem valuable? Here, a bevy of practical considerations come to mind: one formulation might be faster, less complicated, or use more familiar concepts. According to "instrumentalism," these practical benefits are all there is to reformulating. Some reformulations are simply more instrumentally valuable for meeting the aims of science than others. At another extreme, "fundamentalism" contends that a reformulation is valuable when it provides a more fundamental description of reality. According to this view, some reformulations directly contribute to the metaphysical aim of carving reality at its joints. Conceptualism develops a middle ground between instrumentalism and fundamentalism, preserving their benefits without their costs. I argue that the epistemic value of significant reformulations does not reduce to either practical or metaphysical value. Reformulations are valuable because they are a constitutive part of problem-solving. Both science and mathematics aim at solving all possible problems within their respective domains. Meeting this aim requires being able to plan for any possible problem-solving context, and this requires reformulating. By reformulating, we clarify what we need to know to solve problems. Still, one might wonder whether the value of reformulations requires underlying differences in explanatory power. According to "explanationism," a reformulation is valuable only when it provides a better explanation. Explanationism stands as a rival middle ground position to my own. However, it faces numerous counterexamples. In many cases, two reformulations provide the same explanation while nonetheless providing different ways of understanding a phenomenon. Hence, reformulating can be valuable even when neither formulation is more explanatory. Methodologically, I draw on a variety of case studies to support my account of reformulation. These range from classical mechanics to quantum chemistry, along with examples from mathematics. Symmetry arguments provide a paradigmatic example: the mathematics of symmetry groups radically recasts quantum mechanics and quantum chemistry. Nevertheless, elementary approaches exist that eschew this additional mathematical apparatus, solving problems in a more tedious but less mathematically-demanding manner. Further examples include reformulations of quantum field theory, Arabic vs. Roman numerals, and Fermat's little theorem in number theory. In each case, my account identifies how reformulations change and improve our understanding of science and mathematics. (shrink)

In this paper a symmetry argument against quantity absolutism is amended. Rather than arguing against the fundamentality of intrinsic quantities on the basis of transformations of basic quantities, a class of symmetries defined by the Π-theorem is used. This theorem is a fundamental result of dimensional analysis and shows that all unit-invariant equations which adequately represent physical systems can be put into the form of a function of dimensionless quantities. Quantity transformations that leave those dimensionless quantities invariant are empirical (...) and dynamical symmetries. The proposed symmetries of the original argument fail to be both dynamical and empirical symmetries and are open to counterexamples. The amendment of the original argument requires consideration of the relationships between quantity dimensions. The discussion raises a pertinent issue: what is the modal status of the constants of nature which figure in the laws? Two positions, constant necessitism and constant contingentism, are introduced and their relationships to absolutism and comparativism undergo preliminary investigation. It is argued that the absolutist can only reject the amended symmetry argument by accepting constant necessitism. I argue that the truth of an epistemically open empirical hypothesis would make the acceptance of constant necessitism costly: together they entail that the facts are nomically necessary. (shrink)

In addressing the Lucretian symmetry problem, the content-based approach attends to the difference between the contents of the actual life and those of relevant possible lives of a person. According to this approach, the contents of a life with an earlier beginning would substantially differ from, and thus be discontinuous with, the contents of the actual life, whereas the contents of a life with the same beginning but a later death would be continuous with the contents of the actual (...) life. In this paper, I examine two versions of the content-based approach: the identity account and the preference account. The identity account holds that, in the sense of identity which is relevant to the evil of nonexistence, the subject of the actual life, though identical to the person in the life with a later death, is distinct from the subject of the life with an earlier beginning. The preference account maintains that, given one’s attachments to actual particulars, a life with an earlier beginning is not rationally preferable to one’s actual life, whereas a life with a later death is. I argue that each version of the content-based approach is implausible, while discussing some of the complications that face each of them. (shrink)

James Henry Collin recently developed a new symmetry breaker favouring the ontological argument’s possibility premiss over that of the reverse ontological argument. The symmetry breaker amounts to an undercutting defeater for the reverse possibility premiss based on Kripkean cases of a posteriori necessity. I argue, however, that symmetry re-arises in two forms. First, I challenge the purported asymmetry in epistemic entitlements to the original and reverse possibility premisses. Second, relevantly similar Kripkean cases equally undercut the original possibility (...) premiss. (shrink)

Bertrand Russell famously argued that causation is not part of the fundamental physical description of the world, describing the notion of cause as “a relic of a bygone age”. This paper assesses one of Russell’s arguments for this conclusion: the ‘Directionality Argument’, which holds that the time symmetry of fundamental physics is inconsistent with the time asymmetry of causation. We claim that the coherence and success of the Directionality Argument crucially depends on the proper interpretation of the ‘ (...) time symmetry’ of fundamental physics as it appears in the argument, and offer two alternative interpretations. We argue that: if ‘ time symmetry’ is understood as the time -reversal invariance of physical theories, then the crucial premise of the Directionality Argument should be rejected; and if ‘ time symmetry’ is understood as the temporally bidirectional nomic dependence relations of physical laws, then the crucial premise of the Directionality Argument is far more plausible. We defend the second reading as continuous with Russell’s writings, and consider the consequences of the bidirectionality of nomic dependence relations in physics for the metaphysics of causation. (shrink)

It is tempting to think that a process of choosing a point at random from the surface of a sphere can be probabilistically symmetric, in the sense that any two regions of the sphere which differ by a rotation are equally likely to include the chosen point. Isaacs, Hájek, and Hawthorne (2022) argue from such symmetry principles and the mathematical paradoxes of measure to the existence of imprecise chances and the rationality of imprecise credences. Williamson (2007) has argued from (...) a related symmetry principle to the failure of probabilistic regularity. We contend that these arguments fail, because they rely on auxiliary assumptions about probability which are inconsistent with symmetry to begin with. We argue, moreover, that symmetry should be rejected in light of this inconsistency, and because it has implausible decision- theoretic implications. -/- The weaker principle of probabilistic invariance says that the probabilistic comparison of any two regions is unchanged by rotations of the sphere. This principle supports a more compelling argument for imprecise probability. We show, however, that invariance is incompatible with mundane judgments about what is probable. Ultimately, we find reason to be suspicious of the application of principles like symmetry and invariance to nonmeasurable regions. (shrink)

Much recent philosophy of physics has investigated the process of symmetry breaking. Here, I critically assess the alleged symmetry restoration at the fundamental scale. I draw attention to the contingency that gauge symmetries exhibit, that is, the fact that they have been chosen from an infinite space of possibilities. I appeal to this feature of group theory to argue that any metaphysical account of fundamental laws that expects symmetry restoration up to the fundamental level is not fully (...) satisfactory. This is a symmetry argument in line with Curie’s first principle. Further, I argue that this same feature of group theory helps to explain the ‘unreasonable’ effectiveness of mathematics in physics, and that it reduces the philosophical significance that has been attributed to the objectivity of gauge symmetries. (shrink)

Science frequently gives us multiple, compatible ways of solving the same problem or formulating the same theory. These compatible formulations change our understanding of the world, despite providing the same explanations. According to what I call "conceptualism," reformulations change our understanding by clarifying the epistemic structure of theories. I illustrate conceptualism by analyzing a typical example of symmetry-based reformulation in chemical physics. This case study poses a problem for "explanationism," the rival thesis that differences in understanding require ontic explanatory (...) differences. To defend conceptualism, I consider how prominent accounts of explanation might accommodate this case study. I argue that either they do not succeed, or they generate a skeptical challenge. (shrink)

This paper has three main objectives: (a) Discuss the formal analogy between some important symmetry-invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy principle in probability theory, and de Finetti-type theorems in Bayesian statistics; (b) Discuss the epistemological and ontological implications of these theorems, as they are interpreted in physics and statistics. Specifically, we will focus on the positivist (in physics) or subjective (in statistics) interpretations vs. objective (...) interpretations that are suggested by symmetry and invariance arguments; (c) Introduce the cognitive constructivism epistemological framework as a solution that overcomes the realism-subjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion. (shrink)

An agent is morally competent if she can respond to moral considerations. There is a debate about whether agents are open to moral blame only if they are morally competent, and Dana Nelkin’s “Psychopaths, Incorrigible Racists, and the Faces of Responsibility” is an important contribution to this debate. Like others involved in this dispute, Nelkin takes the case of the psychopath to be instructive. This is because psychopaths are similar to responsible agents insofar as they act deliberately and on judgments (...) about reasons, and yet psychopaths lack moral competence. Nelkin argues that, because of their moral incompetence, vices such as cruelty are not attributable to psychopaths. It follows that psychopaths are not open to moral blame since their behavior is only seemingly vicious. I have three aims in this reply to Nelkin. First, I respond to her claim that psychopaths are not capable of cruelty. Second, I respond to the related proposal—embedded in Nelkin’s “symmetry argument”—that a “pro-social psychopath” would not be capable of kindness. My responses to these claims are unified: even if the psychopath is not capable of “cruelty,” and the pro-social psychopath is not capable of “kindness,” the actions of these agents can have a significance for us that properly engages our blaming and praising practices. Finally, I argue that Nelkin’s strategy for showing that moral competence is required for cruelty supports a stronger conclusion than she anticipates: it supports the conclusion that blameworthiness requires not just moral competence, but actual moral understanding. (shrink)

A prima facie plausible and widely held view in epistemology is that the epistemic standards governing the acquisition of testimonial knowledge are stronger than the epistemic standards governing the acquisition of perceptual knowledge. Conservatives about testimony hold that we need prior justification to take speakers to be reliable but recognise that the corresponding claim about perception is practically a non-starter. The problem for conservatives is how to establish theoretically significant differences between testimony and perception that would support asymmetrical epistemic standards. (...) In this paper I defend theoretical symmetry of testimony and perception on the grounds that there are no good reasons for taking these two belief forming methods to have significant theoretical differences. I identify the four central arguments in defence of asymmetry and show that in each case either they fail to establish the difference that they purport to establish or they establish a difference that is not theoretically significant. (shrink)

One of the most influential arguments against the claim that computers can think is that while our intentionality is intrinsic, that of computers is derived: it is parasitic on the intentionality of the programmer who designed the computer-program. Daniel Dennett chose a surprising strategy for arguing against this asymmetry: instead of denying that the intentionality of computers is derived, he endeavours to argue that human intentionality is derived too. I intend to examine that biological plausibility of Dennett’s suggestion and (...) show that Dennett’s argument for the claim that human intentionality is derived because it was designed by natural selection is based on the misunderstanding of how natural selection works. (shrink)

Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space of possible dynamical models in such a way that forces and charges are appropriately coupled. We review the most well-known application of this kind, known as the 'gauge argument' or 'gauge principle', discuss its difficulties, and then reconstruct the (...) gauge argument as a valid theorem in quantum theory. We then present what we take to be a better and more general gauge argument, based on Noether's second theorem in classical Lagrangian field theory, and argue that this provides a more appropriate framework for understanding how gauge symmetry helps to constrain the dynamics of physical theories. (shrink)

In this paper I prove that holistic coherentism is logically equivalent to the conjunction of symmetry and quasi-transitivity of epistemic support and a condition on justified beliefs. On the way I defend Tom Stoneham from a criticism made by Darrell Rowbottom and prove a premiss of Stoneham’s argument to be an entailment of coherentism.

In addressing the Lucretian symmetry problem, the temporal bias approach claims that death is bad because it deprives us of something about which it is rational to care (e.g., future pleasures), whereas prenatal nonexistence is not bad because it only deprives us of something about which it is rational to remain indifferent (e.g., past pleasures). In a recent contribution to the debate on this approach, Miguel and Santos argue that a late beginning can deprive us of a future pleasure. (...) Their argument is based on the claim that for birth or death to deprive a person of any value in life, the historically closest counterfactual situation that contains the value is such that the person begins to exist earlier or dies later. This is what they call the Historical Condition. However, the Historical Condition is untenable for several reasons. First, this condition substantially weakens the explanatory capacity of the deprivation account because it implies that most ordinary sorts of pleasures are not deprived by death. In addition, the Historical Condition is vulnerable to counterexamples. In particular, what they offer as a standard case of the deprivation of future pleasure due to a late beginning (what they call Seeing The Beatles), or some of its variants, can be used to falsify this condition. Finally, the Historical Condition is theoretically indefensible because it is based on a faulty analysis of deprivation. (shrink)

Discusses the symmetry argument in Lucretius and defends the Epicurean claim against objections by Nagel and Parfit. Concludes that while the argument is vulnerable to the objection (found in Nabokov) that treating our past and future non-existence symmetrically leaves open the possiblity of increasing our anxieties rather than eliminating them, it remains rational, on Epicurean grounds, not do to so. In the context of Lucretius's overall argument in DRN 3, it bolsters the claim that we do not have a (...) bias toward the future when we talk about states we do not experience. (shrink)

The classical arguments for scepticism about the external world are defended, especially the symmetry argument: that there is no reason to prefer the realist hypothesis to, say, the deceitful demon hypothesis. This argument is defended against the various standard objections, such as that the demon hypothesis is only a bare possibility, does not lead to pragmatic success, lacks coherence or simplicity, is ad hoc or parasitic, makes impossible demands for certainty, or contravenes some basic standards for a conceptual (...) or linguistic scheme. Since the conclusion of the sceptical argument is not true, it is concluded that one can only escape the force of the argument through some large premise, such as an aptitude of the intellect for truth, if necessary divinely supported. (shrink)

For Tarski talk about the truth in a language, and not generate contradictions, it requires doing it from a different language with greater expressive power: the metalanguage. So, a metalanguage is a language that is used to talk about another language. In scientific language this distinction is very important. In physics, the notion of symmetry is shown through the language used within physical theories. In this way, through algebraic language ─automorphism─ we shown the symmetry ─invariancia, order, equilibrium─ finding (...) (within the language of these theories) the use of the notion sometimes as a principle and sometimes as argument. The distinction in use of the notion of symmetry, on the part of physics, allows us to glimpse symmetry as a term of the metalanguage. Through a brief historical reconstruction ─from the Greeks to present time─ we show the notion of symmetry as a metalanguage term distinguishing the use ─principle and argument─ that physics makes of the concept. Keywords: symmetry, automorphism, principle, argument. (shrink)

Death can be bad for an individual who has died, according to the “deprivation approach,” by depriving that individual of goods. One worry for this account of death’s badness is the Lucretian symmetry argument: since we do not regret having been born later than we could have been born, and since posthumous nonexistence is the mirror image of prenatal nonexistence, we should not regret dying earlier than we could have died. Anthony Brueckner and John Martin Fischer have developed a (...) response to the Lucretian challenge by arguing that it is rational to have asymmetric attitudes toward posthumous and prenatal nonexistence. Recently, Jens Johansson has criticized the Brueckner/Fischer position, claiming that it is irrelevant whether it is actually rational to care about future pleasures but not past pleasures. What matters, according to Johansson, is whether it would be rational for us to care about past pleasures had we come into existence earlier. In this paper, I add to the conversation between Johansson and Brueckner/Fischer by suggesting a way to defend the latter side’s position in a way that has not yet been suggested. I do this by considering a suggestion of Johansson’s for interpreting the Brueckner/Fischer position and by arguing that Johansson’s worry for the position I consider is actually incoherent. (shrink)

Do the facts of evolution generate an epistemic challenge to moral realism? Some think so, and many “evolutionary debunking arguments” have been discussed in the recent literature. But they are all murky right where it counts most: exactly which epistemic principle is meant to take us from evolutionary considerations to the skeptical conclusion? Here, I will identify several distinct species of evolutionary debunking argument in the literature, each one of which relies on a distinct epistemic principle. Drawing on recent (...) work in epistemology, I will show that most of these initially plausible principles are false, spoiling the arguments that rely on them. And we will see that each argument threatens only one popular view of moral psychology: a “Representationalist” view on which our moral judgments rely crucially on a mental intermediary—e.g. a sentiment, gut reaction, or affect-laden intuition—delivered by our evolved moral faculty. In the end, only one evolutionary debunking argument remains a menace: an “ Argument from Symmetry ” that I will introduce to the literature. But we will see that it should worry only all naturalists, pressuring them into a trilemma: give up moral realism, accept a rationalism that is incongruous with naturalism, or give up naturalism. Non-naturalists are free and clear. (shrink)

A primary argument against the badness of death (known as the Symmetry Argument) appeals to an alleged symmetry between prenatal and posthumous nonexistence. The Symmetry Argument has posed a serious threat to those who hold that death is bad because it deprives us of life’s goods that would have been available had we died later. Anthony Brueckner and John Martin Fischer develop an influential strategy to cope with the Symmetry Argument. In their attempt to break the (...) symmetry, they claim that due to our preference of future experiential goods over past ones, posthumous nonexistence is bad for us, whereas prenatal nonexistence is not. Granting their presumption about our preference, however, it is questionable that prenatal nonexistence is not bad. This consideration does not necessarily indicate their defeat against the Symmetry Argument. I present a better response to the Symmetry Argument: the symmetry is broken, not because posthumous nonexistence is bad while prenatal nonexistence is not, but because (regardless as to whether prenatal nonexistence is bad) posthumous nonexistence is even worse. (shrink)

I outline a heretofore neglected difference between manipulation scenarios and merely deterministic ones. Plausible scientific determinism does not imply that the relevant prior history of the universe is independent of us, while manipulation does. Owing to sensitive dependence of physical outcomes upon initial conditions, in order to trace a deterministic history, a microphysical level of analysis is required. But on this level physical laws are time-symmetrically deterministic, and causality, conceived asymmetrically, disappears. I then consider a revised scenario to resurrect the (...) threat of manipulation even in the presence of time-symmetry and sensitive dependence upon initial conditions. To do so we posit a manipulator containing all the information of the manipulated and time-symmetrically related to him. The new scenario violates special relativity, but even waiving that objection, the scenario faces a dilemma. I argue that the manipulator either lacks agency enough to manipulate the target, or can integrate thoughts separated by long time spans into a single decision. In the latter case, the 'manipulated agent' disappears into the manipulator, making it the story of just one agent. (shrink)

In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non- Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement many physicists, Galilei invariance (...) is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function. (shrink)

The most popular philosophical account of how death can harm (or be bad for) the deceased is the deprivation account, according to which death is bad insofar as it deprives the deceased of goods that would have been enjoyed by that person had the person not died. In this paper, the author surveys four main challenges to the deprivation account: the No-Harm-Done Argument, the No-Subject Argument, the Timing Argument, and the Symmetry Argument. These challenges are often raised by Epicureans, (...) who (following Epicurus) claim that death cannot harm the deceased, and each challenge is addressed in Thomas Nagel’s classic essay, “Death,” which has been very influential on recent developments in the literature on the philosophy of death. The author of this paper summarizes some of these recent developments as the challenges are considered. (shrink)

One of the most fascinating and continually debated arguments in the philosophical literature on the badness of death comes from the work of Lucretius (Titus Lucretius Carus, circa 99-55 BCE). This chapter will focus on Lucretius’s famous Symmetry Argument. I will begin by saying more about what exactly Epicureanism teaches about death — and why Epicureans thought it could not be bad. After that, I will provide the passage from Lucretius’s epic poem that includes his reasons for thinking (...) that death cannot be bad and will show how Lucretius’s passage has been regimented into the Symmetry Argument against the badness of death. Next, I will discuss the lasting influence of Lucretius’s argument, summarizing some common ways of responding. Finally, I will turn to two other passages from Lucretius’s poem, both of which suggest that it is actually good (both for us and for the world) that our lives come to an end, and I will conclude by considering the implications of Lucretius’s thought for political policy. (shrink)

The presence of symmetries in physical theories implies a pernicious form of underdetermination. In order to avoid this theoretical vice, philosophers often espouse a principle called Leibniz Equivalence, which states that symmetry-related models represent the same state of affairs. Moreover, philosophers have claimed that the existence of non-trivial symmetries motivates us to accept the Invariance Principle, which states that quantities that vary under a theory’s symmetries aren’t physically real. Leibniz Equivalence and the Invariance Principle are often seen as part (...) of the same package. I argue that this is a mistake: Leibniz Equivalence and the Invariance Principle are orthogonal to each other. This means that it is possible to hold that symmetry-related models represent the same state of affairs whilst having a realist attitude towards variant quantities. Various arguments have been presented in favour of the Invariance Principle: a rejection of the Invariance Principle is inter alia supposed to cause indeterminism, undetectability or failure of reference. I respond that these arguments at best support Leibniz Equivalence. (shrink)

The Sleeping Beauty problem remains controversial with disagreement between so-called Halfers and Thirders, although the Thirders appear to be leading these days. I analyze three popular arguments for the Thirder position, including the long-run frequency argument, Egla’s ‘symmetry’ argument, and new-information arguments, and find problems with each. The long-run frequency argument is almost unequivocally thought to strongly support Thirders, but in formalizing the argument for an arbitrary number of repetitions, I show that the expected proportion of Heads-Awakenings (...) for a single-trial experiment is unambiguously 1/2. My criticisms of Elga’s symmetry argument and the new-information arguments point to subtle misalignments between the narrative/causal description of thought-experiments and the mathematical probability expressions and theory we use to describe these narratives. I end with distinguishing two varieties of possibility—a dynamic forward type and static historical type—that help clarify the Sleeping Beauty problem, nullify the main criticism against Lewis’s Halfer argument, and have applicability to probability theory in general. (shrink)

Chrisoula Andreou says procrastination qua imprudent delay is modeled by Warren Quinn’s self-torturer, who supposedly has intransitive preferences that rank each indulgence in something that delays his global goals over working toward those goals and who finds it vague where best to stop indulging. His pair-wise choices to indulge result in his failing the goals, which he then regrets. This chapter argues, contra the money-pump argument, that it is not irrational to have or choose from intransitive preferences; so the agent’s (...) delays are not imprudent, not instances of procrastination. Moreover, the self-torturer case is intelligible only if there is no vagueness and if the agent’s preferences are transitive. But then he would delay only from ordinary weakness of will. And when it is vague where best to stop indulging, rational agents would use symmetry-breaking techniques; so, again, any procrastination would be explained by standard weakness of will, not vagueness. (shrink)

What would it be for a process to happen backwards in time? Would such a process involve different causal relations? It is common to understand the time-reversal invariance of a physical theory in causal terms, such that whatever can happen forwards in time can also happen backwards in time. This has led many to hold that time-reversal symmetry is incompatible with the asymmetry of cause and effect. This article critiques the causal reading of time reversal. First, I argue that (...) the causal reading requires time-reversal-related models to be understood as representing distinct possible worlds and, on such a reading, causal relations are compatible with time-reversal symmetry. Second, I argue that the former approach does, however, raise serious sceptical problems regarding the causal relations of paradigm causal processes and as a consequence there are overwhelming reasons to prefer a non-causal reading of time reversal, whereby time reversal leaves causal relations invariant. On the non-causal reading, time-reversal symmetry poses no significant conceptual nor epistemological problems for causation. _1_ Introduction _1.1_ The directionality argument _1.2_ Time reversal _2_ What Does Time Reversal Reverse? _2.1_ The B- and C-theory of time _2.2_ Time reversal on the C-theory _2.3_ Answers _3_ Does Time Reversal Reverse Causal Relations? _3.1_ Causation, billiards, and snooker _3.2_ The epistemology of causal direction _3.3_ Answers _4_ Is Time-Reversal Symmetry Compatible with Causation? _4.1_ Incompatibilism _4.2_ Compatibilism _4.3_ Answers _5_ Outlook. (shrink)

Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phe- notypes, niches, ecosystems. We wish to argue that the evo- lution of life marks the end of a physics world view of law entailed dynamics. Our considerations depend upon dis- cussing the variability of the very ”contexts of life”: the in- teractions between organisms, biological niches and ecosys- tems. These are ever changing, intrinsically indeterminate and even unprestatable: we do not know ahead of (...) time the ”niches” which constitute the boundary conditions on selec- tion. More generally, by the mathematical unprestatability of the ”phase space”, no laws of mo- tion can be formulated for evolution. We call this radical emergence, from life to life. The purpose of this paper is the integration of variation and diversity in a sound concep- tual frame and situate unpredictability at a novel theoretical level, that of the very phase space. Our argument will be carried on in close comparisons with physics and the mathematical constructions of phase spaces in that discipline. The role of symmetries as invariant preserving transformations will allow us to under- stand the nature of physical phase spaces and to stress the differences required for a sound biological theoretizing. In this frame, we discuss the novel notion of ”enablement”. Life lives in a web of enablement and radical emergence. This will restrict causal analyses to differential cases. Mutations or other causal differ- ences will allow us to stress that ”non conservation princi- ples” are at the core of evolution, in contrast to physical dynamics, largely based on conservation principles as sym- metries. Critical transitions, the main locus of symmetry changes in physics, will be discussed, and lead to ”extended criticality” as a conceptual frame for a better understanding of the living state of matter. (shrink)

There are extensive discussions of the 5D AdS metric that arises naturally from a metric that accounts for the A-series, the B-series, and x^a; black holes, including their information, entropy, temperature, energy, and energy density; the Big Bang; the finitude of singularities here; inflation; AdS/CFT and dS; symmetry groups of this theory of gravity not including and including those of the standard model, with evaluations of how integrated and how plausible they are; how the theory of quantum gravity here (...) gives general relativity in one limit and quantum mechanics in another limit; and much more. -/- Of particular interest is the physics based argument for the continuation of awareness after death, which starts on about page 196 and spans several pages. (shrink)

It may be a myth that Plato wrote over the entrance to the Academy “Let no-one ignorant of geometry enter here.” But it is a well-chosen motto for his view in the Republic that mathematical training is especially productive of understanding in abstract realms, notably ethics. That view is sound and we should return to it. Ethical theory has been bedevilled by the idea that ethics is fundamentally about actions (right and wrong, rights, duties, virtues, dilemmas and so on). That (...) is an error like the one Plato mentions of thinking mathematics is about actions (of adding, constructing, extracting roots and so on). Mathematics is about eternal relations between universals, such as the ratio of the diagonal of a square to the side. Ethics too is about eternal verities, such as the equal worth of persons and just distributions. Mathematical and ethical verities do both constrain actions, such as the possibility of walking over the seven bridges of Königsberg once and once only or of justly discriminating between races. But they are not themselves about action. In principle, neither mathematical nor ethical verities are subject to historical forces or disagreement among tribes (though they can be better understood as time goes on). Plato is right: immersion in mathematics induces an understanding of the necessities underpinning reality, an understanding that is essential for distinguishing objective ethics from tribal custom. Equality, for example, is an abstract concept which is foundational for both mathematics and ethics. (shrink)

De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those that support the other axioms of the probability calculus as compulsory for subjective interpretations. These two lines of reasoning can (...) be reconciled through a slight generalization of the Dutch Book framework. Countable additivity may indeed be abandoned for de Finetti's lottery, but this poses no serious threat to its adoption in most applications of subjective probability. Introduction The de Finetti lottery Two objections to equiprobability 3.1 The ‘No random mechanism’ argument 3.2 The Dutch Book argument Equiprobability and relative betting quotients The re-labelling paradox 5.1 The paradox 5.2 Resolution: from symmetry to relative probability Beyond the de Finetti lottery. (shrink)

Reference in light of Qualia Calculus (QC); Hard Problems in light of QC; The number of qualia in a room in light of QC; verification of 1st-person phenomena; more advanced neurology; 3rd-person and 1st-person aspects of a system; their symmetries; Well-tempered Clavier; the past is not determined; argument for A-theories in light of QC; frames of reference; Standard Model; String Theory; Bach; time; causality; Schrodinger equation; technology; earth; thick present; Zen; the river; free will; materialists in light of QC.

The infamous Hole Argument has led philosophers to develop various versions of substantivalism, of which metric essentialism and sophisticated substantivalism are the most popular. In this journal, Trevor Teitel has recently advanced novel arguments against both positions. However, Teitel does not discuss the position of Jeremy Butterfield, which appeals to Lewisian counterpart theory in order to avoid the Hole Argument. In this note I show that the Lewis-Butterfield view is immune to Teitel’s challenges.

In this paper, I examine the relationship between physicalism and property dualism in the light of the dialectic between anti-physicalist arguments and physicalist responses. Upon rehearsing the moves of each side, it is hard not to notice that there is a puzzling symmetry between dualist attacks on physicalism and physicalist replies. Each position can be developed in a way to defend itself from attacks from the other position, and it seems that there are neither a priori nor a (...) posteriori grounds to choose between the two. I suggest that the reason for the intractability of the disagreement, perhaps surprisingly, is they are both true: physicalism and dualism are formulated in terms of different conceptual schemes, each involving basic metaphysical concepts such as possibility, necessity, law and property. My proposal is that this means that there is no real disagreement in fact; both schemes get at the same reality, in different ways. -/- . (shrink)

ABSTRACT. Two arguments have recently been advanced that Maxwell-Boltzmann particles are indistinguishable just like Bose-Einstein and Fermi-Dirac particles. Bringing modal metaphysics to bear on these arguments shows that ontological indistinguishability for classical (MB) particles does not follow. The first argument, resting on symmetry in the occupation representation for all three cases, fails since peculiar correlations exist in the quantum (BE and FD) context as harbingers of ontic indistinguishability, while the indistinguishability of classical particles remains purely epistemic. The (...) second argument, deriving from the classical limits of quantum statistical partition functions, embodies a conceptual confusion. After clarifying the doctrine of haecceitism, a third argument is considered that attempts to deflate metaphysical concerns altogether by showing that the phase-space and distribution-space representations of MB-statistics have contrary haecceitistic import. Careful analysis shows this argument to fail as well, leaving de re modality unproblematically grounding particle identity in the classical context while genuine puzzlement about the underlying ontology remains for quantum statistics. (shrink)

Varying degrees of symmetry can exist in a social network's connections. Some early online social networks (OSNs) were predicated on symmetrical connections, such as Facebook 'friendships' where both actors in a 'friendship' have an equal and reciprocal connection. Newer platforms -- Twitter, Instagram, and Facebook's 'Pages' inclusive -- are counterexamples of this, where 'following' another actor (friend, celebrity, business) does not guarantee a reciprocal exchange from the other. -/- This paper argues that the basic asymmetric connections in an OSN (...) leads to emergent asymmetrical behaviour in the OSN's overall influence and connectivity, amongst others. This paper will then draw on empirical examples from popular sites (and prior network research) to illustrate how asymmetric connections can render individuals 'voiceless'. -/- The crux of this paper is an argument from the existentialist viewpoint on how the above asymmetric network properties lead to Sartrean bad faith (Sartre, 1943). Instead of genuine interpersonal connection, one finds varying degrees of pressure to assume the Sartrean 'in-itself' (the en soi) mode-of-being, irregardless of the magnitude of 'followers' one has. -/- Finally, this paper poses an open question: what other philosophical issues does this inherent asymmetry in modern social networking give rise to? (shrink)

After long arguments between positivism and falsificationism, the verification of universal hypotheses was replaced with the confirmation of uncertain major premises. Unfortunately, Hemple proposed the Raven Paradox. Then, Carnap used the increment of logical probability as the confirmation measure. So far, many confirmation measures have been proposed. Measure F proposed by Kemeny and Oppenheim among them possesses symmetries and asymmetries proposed by Elles and Fitelson, monotonicity proposed by Greco et al., and normalizing property suggested by many researchers. Based on (...) the semantic information theory, a measure b* similar to F is derived from the medical test. Like the likelihood ratio, measures b* and F can only indicate the quality of channels or the testing means instead of the quality of probability predictions. Furthermore, it is still not easy to use b*, F, or another measure to clarify the Raven Paradox. For this reason, measure c* similar to the correct rate is derived. Measure c* supports the Nicod Criterion and undermines the Equivalence Condition, and hence, can be used to eliminate the Raven Paradox. An example indicates that measures F and b* are helpful for diagnosing the infection of Novel Coronavirus, whereas most popular confirmation measures are not. Another example reveals that all popular confirmation measures cannot be used to explain that a black raven can confirm “Ravens are black” more strongly than a piece of chalk. Measures F, b*, and c* indicate that the existence of fewer counterexamples is more important than more positive examples’ existence, and hence, are compatible with Popper’s falsification thought. (shrink)

I argue for the existence of imaginative beliefs: mental states that are imaginative in format and doxastic in attitude. I advance two arguments for this thesis. First, there are imaginings that play the functional roles of belief. Second, there are imaginings that play the epistemic roles of belief. These arguments supply both descriptive and normative grounds for positing imaginative beliefs. I also argue that this view fares better than alternatives that posit distinct imaginative and doxastic states to account (...) for the same phenomena. Along the way, I demonstrate the theoretical significance of imaginative beliefs by showing how they pose a challenge for standard taxonomies of the mind, clarify the sense in which imagination is occurrent and voluntary, explain the justificatory role of the imagination, and point to a deep but underappreciated symmetry between imagistic and non-imagistic thought. (shrink)

We defend the thesis that every necessarily true proposition is always true. Since not every proposition that is always true is necessarily true, our thesis is at odds with theories of modality and time, such as those of Kit Fine and David Kaplan, which posit a fundamental symmetry between modal and tense operators. According to such theories, just as it is a contingent matter what is true at a given time, it is likewise a temporary matter what is true (...) at a given possible world; so a proposition that is now true at all worlds, and thus necessarily true, may yet at some past or future time be false in the actual world, and thus not always true. We reconstruct and criticize several lines of argument in favor of this picture, and then argue against the picture on the grounds that it is inconsistent with certain sorts of contingency in the structure of time. (shrink)

Rarely does research in the history and philosophy of science lead to new empirical results, but that is exactly what has happened in one of the essays of this special issue: Rang and Grebe-Ellis have developed new experimental techniques to perform measurements Goethe proposed 217 years ago. These measurements fit neatly with Goethe’s idea of polarity—his complementary spectrum is not only an optical, but also a thermodynamical counterpart of Newton’s spectrum. I use the new measurements, firstly, to argue against the (...) asymmetries between light and darkness posited by Lyre and Schreiber; and, secondly, to explicate the alternative theory that Goethe had introduced to urge scientific pluralism. In my replies to exegetical criticism by Böhler, Hampe and Zemplén, I show that the main goal of Goethe’s Farbenlehre was indeed to expose symmetries between light and darkness. Furthermore, I argue that it is worthwhile to focus on the experiments, arguments and hypotheses of the Farbenlehre, and not merely on rhetorical, narrative or stylistical aspects, as Böhler and Hampe would have it. Goethe’s criticism of Newton is often dismissed, but it is in fact surprisingly relevant today. (shrink)

Although physical theories routinely posit absolute quantities, such as absolute position or intrinsic mass, it seems that only comparative quantities such as distance and mass ratio are observable. But even if there are in fact only distances and mass ratios, the success of absolutist theories means that the world looks just as if there are absolute positions and intrinsic masses. If comparativism is nevertheless true, there is a sense in which this is a cosmic conspiracy: the comparative quantities satisfy certain (...) relations that only absolutism can explain. I show that such cosmic conspiracies are a pervasive feature of comparativist theories. The argument is structurally similar to the well-known No Miracles Argument for scientific realism. Just as anti-realism cannot explain the empirical adequacy of our theories in general, so comparativism cannot explain the empirical adequacy of absolutist theories in particular. (shrink)

Radical moral encroachment is the view that belief itself is morally evaluable, and that some moral properties of belief itself make a difference to epistemic rationality. To date, almost all proponents of radical moral encroachment hold to an asymmetry thesis: the moral encroaches on rational belief, but not on rational credence. In this paper, we argue against the asymmetry thesis; we show that, insofar as one accepts the most prominent arguments for radical moral encroachment on belief, one should likewise (...) accept radical moral encroachment on credence. We outline and reject potential attempts to establish a basis for asymmetry between the attitude types. Then, we explore the merits and demerits of the two available responses to our symmetry claim: (i) embracing moral encroachment on credence and (ii) denying moral encroachment on belief. (shrink)

It is tempting to think that multi premise closure creates a special class of paradoxes having to do with the accumulation of risks, and that these paradoxes could be escaped by rejecting the principle, while still retaining single premise closure. I argue that single premise deduction is also susceptible to risks. I show that what I take to be the strongest argument for rejecting multi premise closure is also an argument for rejecting single premise closure. Because of the symmetry (...) between the principles, they come as a package: either both will have to be rejected or both will have to be revised. (shrink)