‎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)

It is commonly argued that the fact that our universe is fine-tuned for life favors both a design hypothesis as well as a non-teleological multiverse hypothesis. The claim that the fine-tuning of this universe supports a non-teleological multiverse hypothesis has been forcefully challenged however by Ian Hacking and Roger White. In this paper we take this challenge even further by arguing that if it succeeds, then not only does the fine-tuning of this universe fail to support a multiverse hypothesis, but (...) it tends to favor a single-universe hypothesis instead. (shrink)

Molinists offer a tempting bargain: accept divine middle knowledge, and reap solutions to a number of philosophical/theological problems. The prime benefit we are meant to reap from middle knowledge is a solution to the problem of freedom and providence. I argue that they cannot deliver. Even if we make metaphysical and semantic assumptions that have generally been considered friendly to Molinism, Molinism is in danger of undermining divine providence altogether. This “collapse" persists despite fairly uncontroversial assumptions, and plagues the best (...) Molinist theories defended in the literature. (shrink)

While it is philosophically contested whether nonlinguistic animals can have conceptual capabilities, it is also philosophically contested whether one can even empirically test for such capabilities. I draw from Sellars’ work on psychological nominalism to develop an empirically tractable means of distinguishing between tasks that require conceptual capabilities and those that do not. Tasks that require conceptual capabilities are those that require awareness of abstract relations, whereas tasks that can be solved merely through Sellarsian picturing do not. I argue that (...) relational matching-to-sample tasks cannot be solved through picturing and therefore require awareness of the abstract relations of same and different. Crows and amazons have both been able to succeed at relational matching-to-sample tasks; therefore, there are at least some nonlinguistic animals that have conceptual capabilities. Finally, I consider the objection that one cannot attribute conceptual capabilities without also attributing knowledge, and Sellarsian conditions for knowledge are beyond the capabilities of any nonlinguistic animal. In response, I argue that Sellarsian conditions for knowledge only require an implicit grasp of the is/looks distinction and empirical work with chimpanzees on their understanding of the appearance/reality distinction demonstrates that they can meet this standard. Therefore, language is not necessary for meeting Sellarsian conditions for knowledge. (shrink)

Can AI systems such as ChatGPT think? We present an argument from rationality for the negative answer to this question. The argument is founded on two central ideas. The first is that if ChatGPT thinks, it is not rational, in the sense that it does not respond correctly to its evidence. The second idea, which appears in several different forms in philosophical literature, is that thinkers are by their nature rational. Putting the two ideas together yields the result that ChatGPT (...) is not a thinker. The paper sets out the argument in detail and shows how it can withstand numerous objections. We end the paper by contrasting the argument from rationality with a more well-known argument often taken to show that ChatGPT doesn’t think, due to Bender and Koller. (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".).

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)

We argue that there is a conflict among classical theism's commitments to divine simplicity, divine creative freedom, and omniscience. We start by defining key terms for the debate related to classical theism. Then we articulate a new argument, the Aloneness Argument, aiming to establish a conflict among these attributes. In broad outline, the argument proceeds as follows. Under classical theism, it's possible that God exists without anything apart from Him. Any knowledge God has in such a world would be wholly (...) intrinsic. But there are contingent truths in every world, including the world in which God exists alone. So, it's possible that God contingently has wholly intrinsic knowledge. But whatever is contingent and wholly intrinsic is an accident. So, God possibly has an accident. This is incompatible with classical theism. Finally, we consider and rebut several objections. (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.

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)

The ecosystem services argument is a highly publicised instrumental argument for protecting biodiversity. I develop a new objection to this argument based on the lack of a causal connection from global species losses to local ecosystem changes. I survey some alternative formulations of services arguments, including ones incorporating option value or a precautionary principle, and show that they do not fare much better than the standard version. I conclude that environmental thinkers should rely less on ecosystem services as a means (...) to defend biodiversity, and that attention should be focused on additional types of value which might be attributed to global biodiversity. (shrink)

If what is morally right or wrong were ultimately a function of our opinions, then even such reprehensible actions as genocide and slavery would be morally right, had we approved of them. Many moral philosophers find this conclusion objectionably permissive, and to avoid it they posit a moral reality that exists independently of what anyone thinks. The notion of an independent moral reality has been subjected to meticulous metaphysical, epistemological and semantic criticism, but it is hardly ever examined from a (...) moral point of view. In this essay I offer such a critique. I argue that the appeal to an independent moral reality as a ground for moral obligations constitutes a substantive moral mistake. However, I do not conclude from this that we must therefore embrace the opposite view that moral truths are ultimately dependent on our attitudes. Rather, I suggest that we reject both of these views and answer the classic meta-ethical question “Is what we morally ought to do ultimately a function of our actual attitudes, or determined independently of them?” with Neither. (shrink)

Automated influence is one of the most pervasive applications of artificial intelligence in our day-to-day lives, yet a thoroughgoing account of its associated individual and societal harms is lacking. By far the most widespread, compelling, and intuitive account of the harms associated with automated influence follows what I call the control argument. This argument suggests that users are persuaded, manipulated, and influenced by automated influence in a way that they have little or no control over. Based on evidence about the (...) effectiveness of targeted advertising as well as empirical results about the nature of attentional control, I provide reasons to reject this argument. In turn, I use C. Thi Nguyen’s theory of value collapse to develop a new account of the harmfulness of automated influence. (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)

The nature of pre-reflective self-consciousness—viz., the putative non-inferential self-consciousness involved in unreflective experiences, has become the topic of considerable debate in recent analytic philosophy of consciousness, as it is commonly taken to be what makes conscious mental states first-personally given to its subject. A major issue of controversy in this debate concerns what pre-reflective self-consciousness is an awareness of. Some scholars have suggested that pre-reflective self-consciousness involves an awareness of the experiencing subject. This ‘egological view’ is opposed to the ‘non-egological (...) view’, according to which the subject, in being pre-reflectively self-conscious, is just aware of their own occurrent mental state. In this paper, I argue in favour of the egological view. The argument I develop is a qualified version of a line of reasoning originally provided by Rosenthal and builds on a proper clarification of the ontological status of token mental states. More precisely, I argue that token mental states are structured ‘fact-like’ entities having their subject among their constituents. Accordingly, one cannot be aware of one’s own occurrent mental state without thereby being aware of oneself. (shrink)

Panpsychism is the view that every concrete and unified thing has some form of phenomenal consciousness or experience. It is an age-old doctrine, which, to the surprise of many, has recently taken on new life. In philosophy of mind, it has been put forth as a simple and radical solution to the mind–body problem (Chalmers 1996, 2003;Strawson 2006; Nagel 1979, 2012). In metaphysics and philosophy of science, it has been put forth as a solution to the problem of accounting for (...) the intrinsic nature of the physical itself (Strawson 2006, Seager 2006). In this thesis, I show that panpsychism can also be defended on the basis of an argument from our (arguable) acquaintance with the nature of causation in agency. This argument has made frequent appearances throughout the history of philosophy, with philosophers such as Leibniz, Schopenhauer and James, and I construct and defend an updated version of it. Furthermore, I offer a solution to the combination problem: how can complex (human and animal-type) consciousness result from simple (fundamental particle-type) consciousness? This is generally regarded as the most serious problem facing contemporary panpsychism. I propose that mental combination can be construed as kind causal process culminating in a fusion, and show how this avoids the main difficulties with accounting for mental combination. (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 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)

Supporters of open borders sometimes argue that the state has no pro tanto right to restrict immigration, because such a right would also entail a right to exclude existing citizens for whatever reasons justify excluding immigrants. These arguments can be defeated by suggesting that people have a right to stay put. I present a new form of the exclusion argument against closed borders which escapes this “right to stay put” reply. I do this by describing a kind of exclusion that (...) has not been discussed in depth, which I call “territorial exclusion.” Territorial exclusion is the process according to which the group that wishes to exclude current citizens secedes from the territory in which those citizens reside. I argue that the wrongness of territorial exclusion explains why there is no pro tanto right for a state to exclude immigrants, because otherwise there would be a pro tanto right for the state to kick people out by seceding from the territory they inhabit. Because kicking people out like this is typically wrong, borders cannot be closed. (shrink)

This paper reconstructs the function argument of Aristotle’s Eudemian Ethics 2.1. The argument seeks to define happiness through the method of division; shows that the highest good is better than all four of the goods of the soul, not only two, as commentators have thought; and unlike the Nicomachean argument, makes the highest good definitionally independent of the human function.

In this paper, I do a few things. I develop a (largely) empirical argument against naïve realism (Campbell, Martin, others) and for representationalism. I answer Papineau’s recent paper “Against Representationalism (about Experience)”. And I develop a new puzzle for representationalists.

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)

Various theorists have endorsed the “communication argument”: communicative capacities are necessary for morally responsible agency because blame aims at a distinctive kind of moral communication. I contend that existing versions of the argument, including those defended by Gary Watson and Coleen Macnamara, face a pluralist challenge: they do not seem to sit well with the plausible view that blame has multiple aims. I then examine three possible rejoinders to the challenge, suggesting that a context-specific, function-based approach constitutes the most promising (...) modification of the communication argument. (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)

Common sense suggests that visual consciousness is essential to skilled motor action, but Andy Clark—inspired by Milner and Goodale's dual visual systems theory—has appealed to a wide range of experimental dissociations to argue that such an assumption is false. Critics of Clark's argument contend that the content driving motor action is actually within subjects' experience, just not easily discovered. In this article, I argue that even if such content exists, it cannot be guiding motor action, since a review of current (...) visual neuroscience indicates that the visual brain areas producing conscious representations are distinct from those driving motor action. (shrink)

In this paper, I offer an indirect argument for the Access Theory of privacy. First, I develop a new version of the rival Control Theory that is immune to all the classic objections against it. Second, I show that this new version of the Control Theory collapses into the Access Theory. I call the new version the ‘Negative Control Account’. Roughly speaking, the classic Control Theory holds that you have privacy if, and only if, you can control whether other people (...) know personal information about you. Critics of the Control Theory often give counterexamples, where privacy is either not diminished even though the claimant has lost control, or where privacy is diminished even though the claimant is in control. I argue that none of these alleged counterexamples work against the Negative Control Account. However, this is not a victory for the control theorist, because the Negative Control Account collapses into the Access Theory. The paper thus adds to the recent trend in the literature of favoring the Access Theory over the Control Theory. (shrink)

Speakers assert in order to communicate information. It is natural, therefore, to hold that the content of an assertion is whatever information it communicates to its audience. In cases involving uncertainty about the semantic values of context-sensitive lexical items, moreover, it is natural to hold that the information an assertion communicates to its audience is whatever information audience members are in a position to recover from it by assuming that the proposition it semantically determines is true. This sort of picture (...) corresponds to an influential and widely endorsed theory of assertoric content: diagonalism. I begin by arguing that, despite its intuitive appeal, diagonalism should be rejected because it conflicts with our intuitive judgments about the circumstances in which the contents of speakers’ assertions would be true or false. I then show that the failure of diagonalism requires us to either abandon a familiar way of thinking about information and rational assertion or hold that the content of an assertion is not always the information it communicates. I suggest that we choose the latter horn of this dilemma — assertoric content is better characterized in terms of the commitments speakers undertake than in terms of the information they communicate. (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)

These remarks take up the reflexive problematics of Being and Nothingness and related texts from a metalogical perspective. A mutually illuminating translation is posited between, on the one hand, Sartre’s theory of pure reflection, the linchpin of the works of Sartre’s early period and the site of their greatest difficulties, and, on the other hand, the quasi-formalism of diagonalization, the engine of the classical theorems of Cantor, Gödel, Tarski, Turing, etc. Surprisingly, the dialectic of mathematical logic from its inception through (...) the discovery of the diagonal theorems can be recognized as a particularly clear instance of the drama of reflection according to Sartre, especially in the positing and overcoming of its proper value-ideal, viz. the synthesis of consistency and completeness. Conversely, this translation solves a number of systematic problems about pure reflection’s relations to accessory reflection, phenomenological reflection, pre-reflective self-consciousness, conversion, and value. Negative foundations, the metaphysical position emerging from this translation between existential philosophy and metalogic, concurs by different paths with Badiou’s Being and Event in rejecting both ontotheological foundationalisms and constructivist antifoundationalisms. (shrink)

This paper analyses the anti-reductionist argument from renormalisation group explanations of universality, and shows how it can be rebutted if one assumes that the explanation in question is captured by the counterfactual dependence account of explanation.

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)

This article shows that a slight variation of the argument in Milne 1996 yields the log‐likelihood ratio l rather than the log‐ratio measure r as “the one true measure of confirmation. ” *Received December 2006; revised December 2007. †To contact the author, please write to: Formal Epistemology Research Group, Zukunftskolleg and Department of Philosophy, University of Konstanz, P.O. Box X906, 78457 Konstanz, Germany; e‐mail: franz.huber@uni‐konstanz.de.

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)

In Nicomachean Ethics 1. 7, Aristotle gives a definition of the human good, and he does so by means of the “ ergon argument.” I clear the way for a new interpretation of this argument by arguing that Aristotle does not think that the ergon of something is always the proper activity of that thing. Though he has a single concept of an ergon, Aristotle identifies the ergon of an X as an activity in some cases but a product in (...) others, depending on the sort of thing the X is—for while the ergon of the eye is seeing, the ergon of a sculptor is a sculpture. This alternative interpretation of Aristotle’s concept of an ergon allows the key explanatory middle term of the ergon argument to be what, I argue, it ought to be: “the best achievement of a human.”. (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.

One main challenge of non-platonist philosophy of mathematics is to account for the apparent objectivity of mathematical knowledge. Cole and Feferman have proposed accounts that aim to explain objectivity through the intersubjectivity of mathematical knowledge. In this paper, focusing on arithmetic, I will argue that these accounts as such cannot explain the apparent objectivity of mathematical knowledge. However, with support from recent progress in the empirical study of the development of arithmetical cognition, a stronger argument can be provided. I will (...) show that since the development of arithmetic is (partly) determined by biologically evolved proto-arithmetical abilities, arithmetical knowledge can be understood as maximally intersubjective. This maximal intersubjectivity, I argue, can lead to the experience of objectivity, thus providing a solution to the problem of reconciling non-platonist philosophy of mathematics with the (apparent) objectivity of mathematical knowledge. (shrink)

Proponents of the no-miracles argument contend that scientific realism is “the only philosophy that doesn’t make the success of science a miracle.” Bas van Fraassen argued, however, that the success of our best theories can be explained in Darwinian terms—by the fact they are survivors of a winnowing process in which unsuccessful theories are rejected. Critics of this selectionist explanation complain that while it may account for the fact we have chosen successful theories, it does not explain why any particular (...) one of those theories succeeds. Against this I defend the claim that if selectionists manage to account for the former, they have no burden to account for the latter; the success of any particular one of our best theories might as well be an extraordinary coincidence. I refer to this enhanced selectionist reply as “coincidentalism” and argue that it is a serious but underappreciated response to the no-miracles argument. More generally, I argue the considerations raised in favor of this response show that versions of the no-miracles argument focusing on the success of particular theories are misguided. (shrink)

This article seeks to provide a response to the Aloneness Argument Against Classical Theism proposed by Joseph C. Schmid and Ryan T. Mullins. This response focuses on showing the unsoundness of the argument once the Doctrine of Divine Simplicity is reformulated within the essentialist aspectival framework provided by the Aspectival Account. Formulating a response to this argument will thus also serve the further purpose of providing an extension of the Aspectival Account and a needed revision of the Doctrine of Divine (...) Simplicity, which can aid others in their quest to further clarify the nature of this doctrine. (shrink)