‎A universal schema for diagonalization was popularized by N. S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fit more theorems in the universal‎ ‎schema of diagonalization‎, ‎such as Euclid's proof for the infinitude of the primes and new proofs (...) of G. Boolos (1997) for Cantor's theorem on the non-equinumerosity of a set with its powerset‎. ‎Then‎, ‎in Linear Temporal Logic‎, ‎we show the non-existence of a fixed-point in this logic whose proof resembles the argument of Yablo's paradox (1985‎, ‎1993)‎. ‎Thus‎, ‎Yablo's paradox turns for the first time into a genuine mathematico-logical theorem in the framework of Linear Temporal Logic‎. ‎Again the diagonal schema of the paper is used in this proof; and it is also shown that G. Priest's inclosure schema (1997) can fit in our universal diagonal / fixed-point schema‎. ‎We also show the existence of dominating (Ackermann-like) functions (which dominate a given countable set of functions‎, ‎such as primitive recursive functions) in the schema. (shrink)

In Zettel, Wittgenstein considered a modified version of Cantor’s diagonal argument. According to Wittgenstein, Cantor’s number, different with other numbers, is defined based on a countable set. If Cantor’s number belongs to the countable set, the definition of Cantor’s number become incomplete. Therefore, Cantor’s number is not a number at all in this context. We can see some examples in the form of recursive functions. The definition "f(a)=f(a)" can not decide anything about the value of f(a). The definiton (...) is incomplete. The definition of "f(a)=1+f(a)" can not decide anything about the value of f(a) too. The definiton is incomplete.<br><br>According to Wittgenstein, the contradiction, in Cantor's proof, originates from the hidden presumption that the definition of Cantor’s number is complete. The contradiction shows that the definition of Cantor’s number is incomplete. <br><br>According to Wittgenstein’s analysis, Cantor’s diagonal argument is invalid. But different with Intuitionistic analysis, Wittgenstein did not reject other parts of classical mathematics. Wittgenstein did not reject definitions using self-reference, but showed that this kind of definitions is incomplete.<br><br>Based on Thomson’s diagonal lemma, there is a close relation between a majority of paradoxes and Cantor’s diagonal argument. Therefore, Wittgenstein’s analysis on Cantor’s diagonal argument can be applied to provide a unified solution to paradoxes. (shrink)

Following Post program, we will propose a linguistic and empirical interpretation of Gödel’s incompleteness theorem and related ones on unsolvability by Church and Turing. All these theorems use the diagonal argument by Cantor in order to find limitations in finitary systems, as human language, which can make “infinite use of finite means”. The linguistic version of the incompleteness theorem says that every Turing complete language is Gödel incomplete. We conclude that the incompleteness and unsolvability theorems find limitations in (...) our finitary tool, which is our complete language. (shrink)

In a recent article, Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of study. In practice, this means (...) excluding as inadmissible all those real numbers whose decimal expansions cannot be calculated in as much detail as one would like by some rule. We argue against Ormell that the classical realist account of the continuum has explanatory power in mathematics and should be accepted, much in the same way that "dark matter" is posited by physicists to explain observations in cosmology. In effect, the indefinable real numbers are like the "dark matter" of real analysis. (shrink)

It would be an understatement to say that Russell was interested in Cantorian diagonal paradoxes. His discovery of the various versions of Russell’s paradox—the classes version, the predicates version, the propositional functions version—had a lasting effect on his views in philosophical logic. Similar Cantorian paradoxes regarding propositions—such as that discussed in §500 of The Principles of Mathematics—were surely among the reasons Russell eventually abandoned his ontology of propositions.1 However, Russell’s reasons for abandoning what he called “denoting concepts”, and his (...) rejection of similar “semantic dualisms” such as Frege’s theory of sense and reference—at least in “On Denoting”—made no explicit mention of any Cantorian paradox. My aim in this paper is to argue that such paradoxes do pose a problem for certain theories such as Frege’s, and early Russell’s, about how definite descriptions are meaningful. My first aim is simply to lay out the problem I have in mind. Next, I shall turn to arguing that the theories of descriptions endorsed by Frege and by Russell prior to “On Denoting” are susceptible to the problem. Finally, I explore what responses a.. (shrink)

This paper deploys a Cantor-style diagonal argument which indicates that there is more possible mathematical content than there are propositional functions in Russell and Whitehead's Principia Mathematica and similar formal systems. This technical result raises a historical question: "How did Russell, who was himself an expert in diagonal arguments, not see this coming?" It turns out that answering this question requires an appreciation of Russell's understanding of what logic is, and how he construed the relationship between logic (...) and Principia Mathematica. (shrink)

In order to explain Wittgenstein’s account of the reality of completed infinity in mathematics, a brief overview of Cantor’s initial injection of the idea into set- theory, its trajectory and the philosophic implications he attributed to it will be presented. Subsequently, we will first expound Wittgenstein’s grammatical critique of the use of the term ‘infinity’ in common parlance and its conversion into a notion of an actually existing infinite ‘set’. Secondly, we will delve into Wittgenstein’s technical critique of the concept (...) of ‘denumerability’ as it is presented in set theory as well as his philosophic refutation of Cantor’s Diagonal Argument and the implications of such a refutation onto the problems of the Continuum Hypothesis and Cantor’s Theorem. Throughout, the discussion will be placed within the historical and philosophical framework of the Grundlagenkrise der Mathematik and Hilbert’s problems. (shrink)

To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self--reference. We turn Yablo's paradox, the most challenging paradox in the recent years, into a genuine mathematical theorem in Linear Temporal Logic (LTL). Indeed, Yablo's paradox comes in several varieties; and he showed in 2004 that there are other versions that are equally paradoxical. Formalizing (...) these versions of Yablo's paradox, we prove some theorems in LTL. This is the first time that Yablo's paradox(es) become new(ly discovered) theorems in mathematics and logic. (shrink)

It has been noticed that self-referential, ambiguous definitional formulas are accompanied by complementary self-referential antinomy formulas, which gives rise to contradictions. This made it possible to re-examine ancient antinomies and Cantor’s Diagonal Argument (CDA), as well as the method of nested intervals, which is the basis for evaluating the existence of uncountable sets. Using Georg Cantor’s remark that every real number can be represented as an infinite digital expansion (usually decimal or binary), a simplified system for verifying the (...) definitions of real numbers, subsets, and strings was created - the Cantor Criterion, which allows faulty definitions to be pointed out. For the CDA, the connection of formulas defining objects (real numbers, subsets, strings) from outside the list with supplementary formulas was demonstrated - their indirect and indispensable nature testifies to the lack of unambiguity and gives rise to contradictions for Cantor’s antinomic formulas. Thus, Cantor’s theorem about the higher power of the set of all subsets, using the reductio ad absurdum proof, lost its power and it was indicated that it is necessary to correct the scheme of the Axiom of Specification, which was introduced precisely to exclude antinomies from set theory by excluding from the use of self-referential antinomies and ambiguous supplementary formulas coupled with them identified by the H hypothesis. The method of nested intervals was investigated and it was shown that every real number can be defined by the limit of nested intervals and a countable list of real numbers obtained from a countable pool of all Jules Richard’s texts. (shrink)

In this paper, I introduce an iterative method aimed at exploring numbers within the interval [0, 1]. Beginning with a foundational set, S0, a series of algorithms are employed to expand and refine this set. Each algorithm has its designated role, from incorporating irrational numbers to navigating non-deterministic properties. With each successive iteration, our set grows, and after infinite iterations, its cardinality is proposed to align with that of the real numbers. This work is an initial exploration into this approach, (...) and further investigation is encouraged to understand its full implications and potential. (shrink)

Cantor argued that absolute infinity is beyond mathematical comprehension. His arguments imply that the domain of mathematics cannot be grasped by mathematical means. We argue that this inability constitutes a foundational problem. For Cantor, however, the domain of mathematics does not belong to mathematics, but to theology. We thus discuss the theological significance of Cantor’s treatment of absolute infinity and show that it can be interpreted in terms of negative theology. Proceeding from this interpretation, we refer to the recent debate (...) on absolute generality and argue that the method of diagonalization constitutes a modern version of the vianegativa. On our reading, negative theology can evoke an attitude of humility with respect to the boundedness of the human condition. Along these lines, we think that the foundational problem of mathematics concerning its domain can be addressed through a methodological attitude of humility. (shrink)

The purpose of this note is to present a strong form of the liar paradox. It is strong because the logical resources needed to generate the paradox are weak, in each of two senses. First, few expressive resources required: conjunction, negation, and identity. In particular, this form of the liar does not need to make any use of the conditional. Second, few inferential resources are required. These are: (i) conjunction introduction; (ii) substitution of identicals; and (iii) the inference: From ¬(p (...) ∧ p), infer ¬ p. It is, interestingly enough, also essential to the argument that the ‘strong’ form of the diagonal lemma be used: the one that delivers a term λ such that we can prove: λ = ¬ T(⌈λ⌉); rather than just a sentence Λ for which we can prove: Λ ≡ ¬T(⌈Λ⌉). The truth-theoretic principles used to generate the paradox are these: ¬(S ∧ T(⌈¬S⌉); and ¬(¬S ∧ ¬T(⌈¬S⌉). These are classically equivalent to the two directions of the T-scheme, but they are intuitively weaker. The lesson I would like to draw is: There can be no consistent solution to the Liar paradox that does not involve abandoning truth-theoretic principles that should be every bit as dear to our hearts as the T-scheme. So we shall have to learn to live with the Liar, one way or another. (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)

A new formulation of the Fine-Tuning Argument (FTA) for the existence of God is offered, which avoids a number of commonly raised objections. I argue that we can and should focus on the fundamental constants and initial conditions of the universe, and show how physics itself provides the probabilities that are needed by the argument. I explain how this formulation avoids a number of common objections, specifically the possibility of deeper physical laws, the multiverse, normalisability, whether God would (...) fine-tune at all, whether the universe is too fine-tuned, and whether the likelihood of God creating a life-permitting universe is inscrutable. (shrink)

According to Schopenhauer’s compensation argument for pessimism, the non-existence of the world is preferable to its existence because no goods can ever compensate for the mere existence of evil. Standard interpretations take this argument to be based on Schopenhauer’s thesis that all goods are merely the negation of evils, from which they assume it follows that the apparent goods in life are in fact empty and without value. This article develops a non-standard variant of the standard interpretation, which (...) accepts the relevance of the negativity thesis but rejects that the argument assumes that life’s goods are all empty and valueless. Instead, it argues that whatever value negative goods might possess, they do not have the kind of value to compensate for positive evils. This involves additional development of the negativity thesis and a defence of it against objections from Byron Simmons (2021). (shrink)

I defend J. L. Austin's direct realism against the colour delusion argument by employing epistemic logic to demonstrate that perceiving colours does not necessitate an intermediary such as sense-data, thus preserving the directness of perception.

For A. J. Ayer, the occurrence of delusions confutes the notion that we perceive the world directly. He argues instead that perceptions are caused by immaterial “sense data” which somehow represent the properties of material things to us in our experiences. J. L. Austin systematically rejects Ayer’s claims, arguing that the occurrence of delusions does not preclude the possibility of direct perception, and that, indeed, our normal perception is direct. I challenge both philosophers’ ideas by examining how they deal with (...) the phenomenon of colour. (shrink)

Dutch Book arguments have been presented for static belief systems and for belief change by conditionalization. An argument is given here that a rule for belief change which under certain conditions violates probability kinematics will leave the agent open to a Dutch Book.

Proponents of the public goods argument ('PGA') seek to ground the authority of the state on its putative indispensability as a means of providing public goods. But many of the things we take to be public goods – including many of the goods commonly invoked in support of the PGA – are actually what we might term publicized goods. A publicized good is any whose ‘public’ character results only from a policy decision to make some good freely and universally (...) available. This fact poses complications for the PGA, insofar as the set of possible publicized goods is quite extensive indeed. (shrink)

In this paper we offer a new argument for the existence of God. We contend that the laws of logic are metaphysically dependent on the existence of God, understood as a necessarily existent, personal, spiritual being; thus anyone who grants that there are laws of logic should also accept that there is a God. We argue that if our most natural intuitions about them are correct, and if they are to play the role in our intellectual activities that we (...) take them to play, then the laws of logic are best construed as necessarily existent thoughts -- more specifically, as divine thoughts about divine thoughts. We conclude by highlighting some implications for both theistic arguments and antitheistic arguments. (shrink)

The paper continues my earlier Chat with OpenAI’s ChatGPT with a Focused LLM Experiment (FLEX). The idea is to conduct Large Language Model (LLM) based explorations of certain areas or concepts. The approach is based on crafting initial guiding prompts and then follow up with user prompts based on the LLMs’ responses. The goals include improving understanding of LLM capabilities and their limitations culminating in optimized prompts. The specific subjects explored as research subject matter include a) diagonalization techniques as practiced (...) by Cantor, Turing, Gödel, and the advances, such as the Forcing techniques introduced by Paul Cohen and later investigators, b) Knowledge Hierarchies & Mapping Exercises, c) Discussions of IJ Good’s Speculations Concerning the First Ultraintelligent Machine, AGI, and Super- intelligence. Results suggest variability between major models like ChatGPT-4, Llama-3, Cohere, Sonnet and Opus. Results also point to strong dependence on users’ preexisting knowledge and skill bases. The paper should be viewed as ’raw data’ rather than a polished authoritative reference. (shrink)

The Dutch Book Argument for Probabilism assumes Ramsey's Thesis (RT), which purports to determine the prices an agent is rationally required to pay for a bet. Recently, a new objection to Ramsey's Thesis has emerged (Hedden 2013, Wronski & Godziszewski 2017, Wronski 2018)--I call this the Expected Utility Objection. According to this objection, it is Maximise Subjective Expected Utility (MSEU) that determines the prices an agent is required to pay for a bet, and this often disagrees with Ramsey's Thesis. (...) I suggest two responses to Hedden's objection. First, we might be permissive: agents are permitted to pay any price that is required or permitted by RT, and they are permitted to pay any price that is required or permitted by MSEU. This allows us to give a revised version of the Dutch Book Argument for Probabilism, which I call the Permissive Dutch Book Argument. Second, I suggest that even the proponent of the Expected Utility Objection should admit that RT gives the correct answer in certain very limited cases, and I show that, together with MSEU, this very restricted version of RT gives a new pragmatic argument for Probabilism, which I call the Bookless Pragmatic Argument. (shrink)

Scholars have often thought that a monistic reading of Aristotle’s definition of the human good – in particular, one on which “best and most teleios virtue” refers to theoretical wisdom – cannot follow from the premises of the ergon argument. I explain how a monistic reading can follow from the premises, and I argue that this interpretation gives the correct rationale for Aristotle’s definition. I then explain that even though the best and most teleios virtue must be a single (...) virtue, that virtue could in principle be a whole virtue that arises from the combination of all the others. I also clarify that the definition of the human good aims at capturing the nature of human eudaimonia only in its primary case. (shrink)

This is a completely informal presentation of the ideas behind the diagonal lemma. One really can't see this important result from too many different angles. This one aims at getting the main idea across. (For the cognoscenti, it is in the spirit of Quine's treatment in terms of "appended to its own quotation".).

Much of the discussion surrounding the ethics of abortion has centered around the notion of personhood. This is because many philosophers hold that the morality of abortion is contingent on whether the fetus is a person - though, of course, some famous philosophers have rejected this thesis (e.g. Judith Thomson and Don Marquis). In this article, I construct a novel argument for the immorality of abortion based on the notion of impairment. This argument does not assume that the (...) fetus is a person - indeed, I concede (for the sake of argument) that the fetus is not a person - and hence the morality of abortion is not contingent on whether the fetus is a person. I finish by answering a plethora of objections to my argument, concluding that none of them are successful. (shrink)

Galen Strawson’s Basic Argument is that because self-creation is required to be truly morally responsible and self-creation is impossible, it is impossible to be truly morally responsible for anything. I contend that the Basic Argument is unpersuasive and unsound. First, I argue that the moral luck debate shows that the self-creation requirement appears to be contradicted and supported by various parts of our commonsense ideas about moral responsibility, and that this ambivalence undermines the only reason that Strawson gives (...) for the self-creation requirement. Second, I argue that the self-creation requirement is so demanding that either it is an implausible requirement for a species of true moral responsibility that we take ourselves to have or it is a plausible requirement of a species of true moral responsibility that we have never taken ourselves to have. Third, I explain that Strawson overgeneralizes from instances of constitutive luck that obviously undermine moral responsibility to all kinds of constitutive luck. (shrink)

Derk Pereboom's Four-Case Argument is among the most famous and resilient manipulation arguments against compatibilism. I contend that its resilience is not a function of the argument's soundness but, rather, the ill-gotten gain from an ambiguity in the description of the causal relations found in the argument's foundational case. I expose this crucial ambiguity and suggest that a dilemma faces anyone hoping to resolve it. After a thorough search for an interpretation which avoids both horns of this (...) dilemma, I conclude that none is available. Rather, every metaphysically coherent interpretation invites either a hard- or soft-line reply to Pereboom's argument. I then consider a recharacterization of the dilemma which seems to clear the way for the defence of a revised Four-Case Argument. I address this rejoinder by identifying a still more fundamental problem shared by all viable interpretations of the manipulation cases, showing that each involves a type of manipulation which undermines the victim's agency. Because this diagnosis supports a soft-line reply to every viable interpretation of the argument and can be endorsed by any compatibilist, I consider it the final piece of the Soft-line Solution to the Four-Case Argument. Finally, I suggest a new taxonomy of manipulation arguments, arguing that none that employs the suppressive variety of manipulation found in Pereboom's argument offers a threat to compatibilism. (shrink)

Kant’s “primacy of the practical” doctrine says that we can form morally justified commitments regarding what exists, even in the absence of sufficient epistemic grounds. In this paper I critically examine three different varieties of Kant’s “moral proof” that can be found in the critical works. My claim is that the third variety—the “moral-psychological argument” based in the need to sustain moral hope and avoid demoralization—has some intriguing advantages over the other two. It starts with a premise that more (...) clearly coheres with Kant’s mature account of moral motivation, and it invokes plausible empirical-psychological theses to motivate a commitment to the full-blown classical deity—the result Kant clearly wanted. From the point of view of its structure, I think this third variety of moral argument also has the most by way of contemporary interest. (shrink)

Bird argues that Armstrong’s necessitarian conception of physical modality and laws of nature generates a vicious regress with respect to necessitation. We show that precisely the same regress afflicts Bird’s dispositional-monist theory, and indeed, related views, such as that of Mumford & Anjum. We argue that dispositional monism is basically Armstrongian necessitarianism modified to allow for a thesis about property identity.

Extended reality devices provide users with unprecedented immersive and hybrid perceptual experiences, and users will act their bodies according to the information perceived. This shows that visual perception plays a crucial role in the formation and shaping of self-perception and spatial position. Users have a strong perceptual experience of their physical presence and self-perception in the real world as a result of their avatar perspective based on visual perception in a virtual hybrid environment, as is issued by Chalmers in his (...) "Mirror Argument". However, users can still clearly differentiate their self and spatial experience between virtual and reality. To refute Chalmers' argument regarding perceptual experience in virtual reality, this article proposes a thought experiment called "Mary's Room in the Virtual Reality World" based on the experimental evidence of neuroscience. Finally, a possible future solution to this dilemma is presented. (shrink)

I discuss the argument Aristotle ascribes to Parmenides at Physics 186a23-32. I discuss (i) the reasons why Aristotle considers it as eristic and inconclusive and (i) the solution (lusis) Aristotle proposes against it.

Most readers believe that it is difficult, verging on the impossible, to extract concrete prescriptions from the ethics of Emmanuel Levinas. Although this view is largely correct, Levinas’ philosophy can, with some assistance, generate specific duties on the part of legal actors. In this paper, I argue that the fundamental premises of Levinas’ theory of justice can be used to construct a prohibition against capital punishment. After analyzing Levinas’ concepts of justice, responsibility, and interruption, I turn toward his scattered remarks (...) on legal institutions, arguing that they enable a sense of interruption specific to the legal domain. It is here that we find the conceptual resources most important to my Levinasian abolition. I argue that the interruption of legal justice by responsibility implies what I call the principle of revisability. The principle of revisability states a necessary condition of just legal institutions: To be just, legal institutions must ensure the possibility of revising any and all of their rules, principles, and judgments. From this, the argument against capital punishment easily follows. Execution is a legal act, perhaps the only legal act, that cannot be undone. An application of the principle of revisability to this fact leads to the conclusion that legal institutions cannot justly impose capital punishment. After defending these points at length, I conclude with some observations on the consequences of the principle of revisability for law more generally. (shrink)

A key question in the philosophy of logic is how we have epistemic justification for claims about logical entailment (assuming we have such justification at all). Justification holism asserts that claims of logical entailment can only be justified in the context of an entire logical theory, e.g., classical, intuitionistic, paraconsistent, paracomplete etc. According to holism, claims of logical entailment cannot be atomistically justified as isolated statements, independently of theory choice. At present there is a developing interest in—and endorsement of—justification holism (...) due to the revival of an abductivist approach to the epistemology of logic. This paper presents an argument against holism by establishing a foundational entailment-sentence of deduction which is justified independently of theory choice and outside the context of a whole logical theory. (shrink)

Pereboom’s Four-Case Argument was once considered to be the most powerful of the manipulation arguments against compatibilism. However, because of Demetriou’s :595–617, 2010) response, Pereboom has significantly weakened his argument. Manipulation arguments in general have also been challenged by King : 65–83, 2013). In this paper, I argue that the Four-Case Argument resists both these challenges. One upshot is that Pereboom doesn’t need weaken his argument. Another is that compatibilists still need a response the Four-Case (...) class='Hi'>Argument. And another is that we get a much better understanding of the Four-Case Argument, and of manipulation arguments more generally, than is currently available in the literature. (shrink)

Can we experience emotion without the feeling of accelerated heartbeats, perspiration, or other changes in the body? In his paper “What is an emotion”, William James famously claimed that “if we fancy some strong emotion and then try to abstract from our consciousness of it all the feelings of its bodily symptoms, we find we have nothing left behind” (1884, p. 193). Thus, bodily changes are essential to emotion. This is known as the Subtraction Argument. The Subtraction Argument (...) is still used to support Embodied theories of emotion. Proponents of Disembodied theories, however, have different intuitions regarding the role of bodily changes in the experience of emotion. In order to advance this debate, I conducted a series of studies testing people’s intuitions regarding the Subtraction Argument. Results show that, against James’ claims, most people consider that their hypothetical (Study 1) and actual (Study 2) emotions persist in the absence of bodily feelings. Furthermore, Study 1 found that participants’ responses were not related to individual differences in reflection or interoceptive awareness. These results pose a problem for Embodied theories of emotion and challenge extant explanations for the persistence of emotional experience in cases of impaired interoception. (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)

Predication is an indisputable part of our linguistic behavior. By contrast, the metaphysics of predication has been a matter of dispute ever since antiquity. According to Plato—or at least Platonism, the view that goes by Plato’s name in contemporary philosophy—the truths expressed by predications such as “Socrates is wise” are true because there is a subject of predication (e.g., Socrates), there is an abstract property or universal (e.g., wisdom), and the subject exemplifies the property.1 This view is supposed to be (...) general, applying to all predications, whether the subject of predication is a person, a planet, or a property.2 Despite the controversy surrounding the metaphysics of predication, many theistic philosophers—including the majority of contemporary analytic theists—regard Platonism as extremely attractive. At the same time, however, such philosophers are also commonly attracted to a form of traditional theism that has at its core the thesis that God is an absolutely independent.. (shrink)

In my article "Even if the fetus is not a person, abortion is immoral: The impairment argument" (this journal), I defended what I called “The impairment argument” which purports to show that abortion is immoral. Bruce Blackshaw (2019) has argued that my argument fails on three accounts. In this article, I respond to his criticisms.

This essay examines Gensler's general consistency principle (GR) and its application to the moral permissibility of abortion. The central claim is that applying GR to abortion leads to the conclusion that abortion is morally impermissible. The essay presents two objections to this claim, which challenge the validity of GR and the manner in which it is applied to abortion. The first objection (O1) states that it is impossible to accurately judge the potential of an object to become a rational being, (...) while the second objection (O2) argues that applying GR to abortion involves the invalid use of a set of potential rational beings rather than a specific instance. Both objections reveal difficulties in applying GR to abortion, undermining the claim that using GR results in the moral impermissibility of abortion. (shrink)

Critics of persuasive advertising argue that it undermines the autonomy of consumers by manipulating their desires in morally problematic ways. My aim is this paper is to refine that argument by employing a conception of autonomy that is not at odds with certain forms of manipulation. I argue that the charge of manipulation is not sufficient for condemning persuasive advertising. On my view, manipulation of an agent’s desires through advertising is justifiable in cases where the agent accepts the process (...) through which the desires were developed. I show how the standard manipulation objection proves too much as it would also condemn cases of that kind. I argue that this distinction is especially important when we consider the implications of “new media.” In addition to increasing vulnerability to manipulation, new media have considerable impacts on well-being. By siding with the traditional autonomy argument, we would be compelled to take an implausible stand against all forms of manipulation through advertising, but I suggest that only a proper subset of those cases are morally problematic. This conclusion opens up a space for persuasive advertising that is permissible while nevertheless condemning cases that violate consumers’ autonomy. (shrink)

According to the most common interpretation of the simulation argument, we are very likely to live in an ancestor simulation. It is interesting to ask if some families of simulations are more likely than others inside the space of all simulations. We argue that a natural probability measure is given by computational complexity: easier simulations are more likely to be run. Remarkably this allows us to extract experimental predictions from the fact that we live in a simulation. For instance (...) we show that it is very likely that humanity will not achieve interstellar travel and that humanity will not meet other intelligent species in the universe, in turn explaining the Fermi's Paradox. On the opposite side, experimental falsification of any of these predictions would constitute evidence against our reality being a simulation. (shrink)

We offer a critical assessment of the “exclusion argument” against free will, which may be summarized by the slogan: “My brain made me do it, therefore I couldn't have been free”. While the exclusion argument has received much attention in debates about mental causation (“could my mental states ever cause my actions?”), it is seldom discussed in relation to free will. However, the argument informally underlies many neuroscientific discussions of free will, especially the claim that advances in (...) neuroscience seriously challenge our belief in free will. We introduce two distinct versions of the argument, discuss several unsuccessful responses to it, and then present our preferred response. This involves showing that a key premise – the “exclusion principle” – is false under what we take to be the most natural account of causation in the context of agency: the difference-making account. We finally revisit the debate about neuroscience and free will. (shrink)

This paper offers a short extension of the dialogue between Anselm and the Fool that is contained in "The Ontological Argument Simplified" by Gary Matthews and Lynne Rudder Baker. My extension of the dialogue ends with the Fool proclaiming that "what looks like an argument of elegant simplicity turns out to be no argument at all".

I develop a new reading of Frege’s argument for the indefinability of truth. I concentrate on what Frege literally says in the passage that contains the argument. This literal reading of the passage establishes that the indefinability argument is an arguably sound argument to the following conclusion: provided that the Fregean conception of judgment—which has recently been countered by Hanks—is correct and that truth is a property of truth-bearers, a vicious infinite regress is produced. Given this (...) vicious regress, Frege chooses to reject that truth is a property of truth-bearers. Frege’s choice leads to a unique version of the Fregean conception of judgment. His unique conception of judgment can cope with Hanks’s recent criticisms against the Fregean conception. (shrink)

According to social externalism, it is possible to possess a concept not solely in virtue of one’s intrinsic properties but also in virtue of relations to one’s linguistic community. Derek Ball (2009) argues, in effect, that (i) social externalism extends to our concepts of colour experience and (ii) this fact undermines both the knowledge argument against physicalism and the most popular physicalist response to it, known as the phenomenal concept strategy. I argue that Ball is mistaken about (ii) even (...) granting (i). The knowledge argument and the phenomenal concept strategy might have to be modified to make them consistent with social externalism, but not in fundamental or detrimental ways. (shrink)

Many philosophers, psychologists, and medical practitioners believe that killing is no worse than letting die on the basis of James Rachels's Bare-Difference Argument. I show that his argument is unsound. In particular, a premise of the argument is that his examples are as similar as is consistent with one being a case of killing and the other being a case of letting die. However, the subject who lets die has both the ability to kill and the ability (...) to let die while the subject who kills lacks the ability to let die. Modifying the latter example so that the killer has both abilities yields a pair of cases with morally different acts. The hypothesis that killing is worse than letting die is the best explanation of this difference. (shrink)

Abstract: “Paley before Hume: How Not to Teach the Design Argument” Most philosophy of religion classes discuss the classic design argument for the existence of God, and many of these treat Paley’s Natural Theology (1802) before Hume’s Dialogues Concerning Natural Religion (1779). Following the syllabus of several leading anthologies, I did this for many years, but I now think that is a mistake, because it creates the impression that Hume was responding to Paley. Not only is it obvious (...) on chronological grounds that Hume could not have been responding to Paley; it is just as obvious on textual grounds that the reverse was true: Paley was in fact responding to Hume, and, e.g., carefully crafted a non-analogical version of the argument so as to avoid Hume’s famous criticisms of analogical arguments. (shrink)