We define a model for computing probabilities of right-nested conditionals in terms of graphs representing Markov chains. This is an extension of the model for simple conditionals from Wójtowicz and Wójtowicz. The model makes it possible to give a formal yet simple description of different interpretations of right-nested conditionals and to compute their probabilities in a mathematically rigorous way. In this study we focus on the problem of the probabilities of conditionals; we do not discuss questions concerning logical and metalogical (...) issues such as setting up an axiomatic framework, inference rules, defining semantics, proving completeness, soundness etc. Our theory is motivated by the possible-worlds approach ; however, our model is generally more flexible. In the paper we focus on right-nested conditionals, discussing them in detail. The graph model makes it possible to account in a unified way for both shallow and deep interpretations of right-nested conditionals. In particular, we discuss the status of the Import-Export Principle and PCCP. We briefly discuss some methodological constraints on admissible models and analyze our model with respect to them. The study also illustrates the general problem of finding formal explications of philosophically important notions and applying mathematical methods in analyzing philosophical issues. (shrink)

I explore how agent-regret and its object—faultlessly harming someone—can call for various responses. I look at two sorts of responses. Firstly, I explore responses that respect the agent’s role as an agent. This revolves around a feature of “it was just an accident”—a common response to agent-regret—that has largely gone ignored in the literature: that it can downplay one’s role as an agent. I argue that we need to take seriously the fact that those who have caused harms are genuine (...) agents, to ignore this fails to allow these agents to move on. Secondly, following Sussman and MacKenzie, I explore responses that benefit the victim. I argue that we should strive to understand how to configure these responses in a way that does not blame the agent. To do this I look at the role of actions in our self-understanding, as people who have done particular things. I end by briefly considering the ways in which tort law and restorative justice might help us to understand how to appropriately respond to accidentally harming someone. I urge that we need to take this as a starting point to find a better way to respond to the agents of faultless harms. (shrink)

I argue that sports clubs should be punished for bad behaviour by their fans in a way that affects the club’s sporting success: for example, we are justified in imposing points deductions and competition disqualifications on the basis of racist chanting. This is despite a worry that punishing clubs in such a way is unfair because it targets the sports team rather than the fans who misbehaved. I argue that this belies a misunderstanding of the nature of sports clubs and (...) of the nature of sporting success. Further, I argue that fans should want to be held responsible in such a way because it vindicates the significant role that they play in the life of their club. (shrink)

This is a book symposium on Why It’s OK to Be a Sports Fan, by Alfred Archer and Jake Wojtowicz, with contributions from Adam Kadlac, Joe Slater, Nathaniel Baron-Schmitt, and Nina Windgätter. The discussion covers a range of topics, including the form of love involved in fandom, the epistemic status of fans, fictionalism, and the role of communities in fandom.

One of central problems in the theory of conditionals is the construction of a probability space, where conditionals can be interpreted as events and assigned probabilities. The problem has been given a technical formulation by van Fraassen (23), who also discussed in great detail the solution in the form of Stalnaker Bernoulli spaces. These spaces are very complex – they have the cardinality of the continuum, even if the language is finite. A natural question is, therefore, whether a technically simpler (...) (in particular finite) partial construction can be given. In the paper we provide a new solution to the problem. We show how to construct a finite probability space $$\mathrm {S}^\#=\left(\mathrm\Omega^\#,\mathrm\Sigma^\#,\mathrm P^\#\right)$$ S # = Ω #, Σ #, P # in which simple conditionals and their Boolean combinations can be interpreted. The structure is minimal in terms of cardinality within a certain, naturally defined class of models – an interesting side-effect is an estimate of the number of non-equivalent propositions in the conditional language. We demand that the structure satisfy certain natural assumptions concerning the logic and semantics of conditionals and also that it satisfy PCCP. The construction can be easily iterated, producing interpretations for conditionals of arbitrary complexity. (shrink)

This is a book symposium on Why It’s OK to Be a Sports Fan, by Alfred Archer and Jake Wojtowicz, with contributions from Adam Kadlac, Joe Slater, Nathaniel Baron-Schmitt, and Nina Windgätter. The discussion covers a range of topics, including the form of love involved in fandom, the epistemic status of fans, fictionalism, and the role of communities in fandom.

In “Voluntary Acts and Responsible Agents,” Bernard Williams sketches what it means to be a mature agent. This mature agent tries to make sense of their own life, which is a life that is shared wit...

I explore what BernardWilliams means by regarding one’s action ‘purely externally, as one might regard anyone else’s action’, and how it links to regret and agent-regret. I suggest some ways that we might understand the external view: as a failure to recognize what one has done, in terms of Williams’s distinction between intrinsic and extrinsic luck, and as akin to Thomas Nagel’s distinction between an internal and external view. I argue that none of these captures what Williams was getting at (...) because they do not allow one to take a view on one’s action. I offer two alternative accounts. One turns around what we identify with, the other concerns what we care about. Both accounts capture how I might regret, rather than agent-regret, my own action. I demonstrate that these accounts can explain the relationship between an insurance payout and the external view, and they can explain the agent-relativity of agent-regret. (shrink)

We define a semantics for conditionals in terms of stochastic graphs which gives a straightforward and simple method of evaluating the probabilities of conditionals. It seems to be a good and useful method in the cases already discussed in the literature, and it can easily be extended to cover more complex situations. In particular, it allows us to describe several possible interpretations of the conditional and to formalize some intuitively valid but formally incorrect considerations concerning the probabilities of conditionals under (...) these two interpretations. It also yields a powerful method of handling more complex issues. The stochastic graph semantics provides a satisfactory answer to Lewis’s arguments against the PC = CP principle, and defends important intuitions which connect the notion of probability of a conditional with the notion of conditional probability. It also illustrates the general problem of finding formal explications of philosophically important notions and applying mathematical methods in analyzing philosophical issues. (shrink)

According to the PCCP thesis, the probability of a conditional A → C is the conditional probability P. This claim is undermined by Lewis’ triviality results, which purport to show that apart from trivial cases, PCCP is not true. In the present article we show that the only rational, “Dutch Book-resistant” extension of the agent’s beliefs concerning non-conditional sentences A and C to the conditional A → C is by assuming that P = P. In other cases a diachronic Dutch (...) Book against the agent can be constructed. There is a tension between our findings and Lewis’ results, which needs to be explained. Therefore, we present a probability space which corresponds in a natural way to the diachronic Dutch Book—and which allows the conditional A → C to be interpreted as an event in a mathematically sound way. It also allows to formalize the notion of conditionalizing A → C on ¬C which plays a crucial role in Lewis’ proof. Our conclusion is that Lewis’ proof is circular, so it cannot be considered to be a sound argument against PCCP. (shrink)

When sporting agents fail through wrongful or faulty behaviour, they should feel guilty; when they fail because of a deficiency in their abilities, they should feel shame. But sometimes we fail without being deficient and without being at fault. I illustrate this with two examples of players, Moacir Barbosa and Roberto Baggio, who failed in World Cup finals and cost their teams the greatest prize in sport. Although both players failed, I suggest that neither was at fault and neither was (...) deficient. I argue that we can fail through no fault of our own because our abilities are always fallible. This fallibility means that to succeed – to achieve sporting glory – we must run the risk of failure. The appropriate emotion to feel over such failures is agent-regret. Sporting agents and observers should not take up what I call the ‘critical position’: the idea that someone who fails must be deficient or must have been at fault. This allows for a softer, but also more accurate, attitude towards our own failures and the failures of others. I end by suggesting that the fallibility of our abilities is made clear through playing or watching sport, and this can illuminate life more broadly. (shrink)

In this letter, we argue that an economic perspective on the mind has played—and should continue to play—a central role in the development of cognitive science. Viewing cognition as the productive application of mental resources puts cognitive science and economics on a common conceptual footing, paving the way for closer collaboration between the two disciplines. This will enable cognitive scientists to more readily repurpose economic concepts and analytical tools for the study of mental phenomena, while at the same time, enriching (...) our understanding of the modern economy, which is increasingly driven by mental, rather than physical, production. (shrink)

How should sport deal with prematurely ended seasons? This question is especially relevant to the current COVID-19 inter- ruption that threatens to leave many leagues without cham- pions. We argue that although there can be no winners, in certain situations there should be champions. Relevant to the current situation, we argue that Liverpool FC—currently with a 22+ point lead—should be crowned champions of the English Premier League. However, things are not as simple as simply handing the championship to whoever was (...) in the lead when a season is prematurely ended. Through analogy with a fictional decathlon competition—and with the understanding that sporting seasons are themselves a type of game—we identify three reasons why leading at the moment of cessation is insufficient to be crowned a victor (of an individual event) or a champion (of a season-long competition): doing so fails to respect some valuable skills, fails to allow for luck to play out in an interesting way that affects competitions, and fails to respect competitive strategies. This discussion can then inform determining what, if any, end-of-season accolades are relevant, such as championships, relegation, or promotion. No team can win in a league that has failed to be completed, but there can still be a champion. (shrink)

I argue for a novel understanding of the nature of agent-regret. On the standard picture, agent-regret involves regretting the result of one’s action and thus regretting one’s action. I argue that the standard picture is a flawed analysis of agent-regret. I offer several cases of agent-regret where the agent feels agent-regret but does not regret the result itself. I appeal to other cases where an agent’s attitude towards something depends upon whether or not they are involved in that thing. I (...) argue that the same applies to actions: sometimes an agent’s attitude towards a result differs from their attitude to their involvement in bringing about that result. Agent-regret is regret about my own action, but it need not involve regret about something in the world. I end by considering how this picture of agent-regret allows us to respond to a particular criticism of agent-regret. (shrink)

Sporting competitions have been beset by change due to COVID-19. Some commentators and sportspeople worried that this affected the integrity of these competitions. Focussing on European football, I suggest that one way of understanding integrity is in terms of fairness. I argue that many changes introduced a form of luck that is already common and widespread and that many changes were also justified. Thus, they did not affect the integrity of these competitions in this way. I then suggest that there (...) is another integrity issue lurking: that the changes affected the character of these competitions, rendering them unrecognizable. I briefly explore this issue. (shrink)

The inferentialism due to Robert Brandom presents a compelling normative-deontic picture of language and discursive practices, and as such it is well positioned to address phenomena like lying. This short work outlines a simple account of how lying can be conceptualized within that framework. To that end, the basic Brandomian position is extended to include a novel type of status – namely, pseudo-commitments, which are unique in their being non-binding. The traditional definition of lying is then given a status-oriented form, (...) such that lying consists in presenting a pseudo-commitment with the intention for it to be attributed as a standard commitment. Importantly, this can be articulated in our scorekeeping practices, which is demonstrated with three example exchanges – one featuring an undetected lie, one featuring a detected lie, and one featuring a bald-faced lie. Though simple, the account works and invites extension to other similar phenomena, like sarcasm, acting, bullshit, etc. The notion of pseudo-commitment may also find application outside of the inferentialist context. (shrink)

Robots are becoming more visible parts of our life, a situation which prompts questions about their place in our society. One group of issues that is widely discussed is connected with robots’ moral and legal status as well as their potential rights. The question of granting robots rights is polarizing. Some positions accept the possibility of granting them human rights whereas others reject the notion that robots can be considered potential rights holders. In this paper, I claim that robots will (...) never have all human rights, even if we accept that they are morally equal to humans. I focus on the role of embodiment in the content of the law. I claim that even relatively small differences in the ontologies of entities could lead to the need to create new sets of rights. I use the example of Neanderthals to illustrate that entities similar to us might have required different legal statuses. Then, I discuss the potential legal status of human-like robots. (shrink)

Whether or not we call a love-like relationship with robots true love, some people may feel and claim that, for them, it is a sufficient substitute for love relationship. The love relationship between humans has a special place in our social life. On the grounds of both morality and law, our significant other can expect special treatment. It is understandable that, precisely because of this kind of relationship, we save our significant other instead of others or will not testify against (...) her/him. How as a society should we treat love-like relationships humans with robots? Based on the assumption that robots do not have an inner life and are not moral patients, I defend the thesis that this kind of relationship should be protected by criminal law. (shrink)

We analyze three interesting arguments from the literature, where ascribing a probability of 1 to a certain right-nested conditional A→(B→C) leads to strong theses concerning conditionals: they serve as counterexamples to important general claims. The first is the classic and much discussed McGee’s counterexample to Modus Ponens from McGee [“A Counterexample to Modus Ponens.” The Journal of Philosophy 82 (9): 462–471]. The second example was given by Santorio [“Trivializing Informational Consequence.” Philosophy and Phenomenological Research 104:297–320] and is intended to undermine (...) the probabilistic version of Modus Ponens. The third example was presented in Cantwell [“Revisiting McGee’s Probabilistic Analysis of Conditionals.” Journal of Philosophical Logic 51 (5): 973–1017] in order to reject the general version of the Ramsey Test (i.e. PCCP) and Modus Ponens. These examples are based on a specific interpretation of right-nested conditional which is not the only possible one. We provide examples demonstrating that alternative interpretations are feasible. As a result, the arguments presented in the three cited works possess limited efficacy, as they are confined solely to the particular interpretation of the conditional. (shrink)

Artykuł analizuje problem kosztów powstałych w wyniku realizacji obowiązku udzielenia pomocy osobie znajdującej się w niebezpieczeństwie. Autorzy prezentują trzy odmienne stanowiska dotyczące tego problemu, rozważając scenariusz, w którym osoba decyduje się, z własnej woli lub przymuszona za pomocą prawa, uratować inną osobę, w sytuacji, w której taka pomoc wiąże się z naruszeniem praw trzeciej strony. Przykładowo, A ratuje tonącego B, ale w trakcie ratowania narusza prawa C. Pytanie, które stawiają autorzy brzmi: zakładając, że istnieje obowiązek udzielenia pomocy osobie znajdującej się (...) w niebezpieczeństwie, kto powinien ponieść koszty odszkodowania za naruszenie praw trzeciej strony? Autorzy rozważają następujące możliwości: koszty pomocy powinny zostać poniesione przez (a) ratującego, (b) osobę, której prawa zostały naruszone, (c) ratowanego, (d) całe społeczeństwo. (shrink)

Although mathematical philosophy is flourishing today, it remains subject to criticism, especially from non-analytical philosophers. The main concern is that even if formal tools serve to clarify reasoning, they themselves contribute nothing new or relevant to philosophy. We defend mathematical philosophy against such concerns here by appealing to its metaphysical foundations. Our thesis is that mathematical philosophy can be founded on the phenomenological theory of ideas as developed by Roman Ingarden. From this platonist perspective, the “unreasonable effectiveness of mathematics in (...) philosophy”—to adapt Wigner’s phrase—is analogous to that of mathematical explanations in science. As success-criteria for mathematical philosophy, we propose that it should be correct, responsive, illuminating, promising, relevant, and adequate. (shrink)

PCCP is the much discussed claim that the probability of a conditional A → B is conditional probability. Triviality results purport to show that PCCP – as a general claim – is false. A particularly interesting proof has been presented in (Hájek, 2011), who shows that – even if a probability distribution P initially satisfied PCCP – a rational update can produce a non-PCCP probability distribution. We argue that the notion of rational update in this argumentation is construed in much (...) too broad a way. In order to make the argumentation precise, we discuss the general rules for modeling conditionals in probability spaces and present formalized version(s) of PCCP and of minimal assumptions concerning the appropriate spaces. Using the introduced apparatus we give a detailed analysis of Hájek’s (2011) triviality proof and show that it is based on an application of revision rules which allow one to construct probability distributions violating not only PCCP, but also fundamental properties of conditionals. This means that they do not really provide arguments against PCCP, properly formalized. We also discuss a Dutch Book argument which shows that the updated belief system is not coherent. This gives an additional, strong argument against accepting the update rules. We also discuss the Converse Dutch Book theorem and argue, that even if the produced probability measure seems to violate it, it cannot serve as the counterexample, as it is not an appropriate model for conditionals. Ultimately, we show that important arguments against PCCP fail. (shrink)

The direct proof of transcendental idealism, in the Transcendental Aesthetic of Kant's First Critique, has borne the brunt of enormous criticism. Much of this criticism has arisen from a confusion regarding the epistemological nature of the arguments Kant proposes with the alleged ontological conclusions he draws. In this paper I attempt to deflect this species of criticism. I concentrate my analysis on the Metaphysical Expositions of Space and Time. I argue that the argument form of the Metaphysical Expositions is that (...) of disjunctive syllogism and that Kant's primary target of attack is that of Leibnizian relativism. I provide a detailed analysis and reconstruction of the arguments of the Metaphysical Expositions, defending Kant against various claims of argumentative invalidity and incoherence. I conclude by identifying what can properly be inferred regarding the ontological nature of space and time, given my reconstructions of the arguments, and by suggesting the manner in which Kant can deflect objections from the other major proponent of transcendental realism, namely, Newtonian absolutism. (shrink)

This dissertation is a defence of agent-regret and an exploration of its role in our lives. I argue that agent-regret shows that an agent takes seriously her status as an agent who impacts the world, but who only has fallible control over it. To accept responsibility for any outcomes, she must accept responsibility for unintended outcomes, too: agent-regret is part of being a human agent. In doing this, I try to defend and develop Williams’s own conception of agent-regret. -/- In (...) the first part, I explore the nature of agent-regret. Agent-regret is distinct from guilt because we can feel agent-regret without being at fault. I argue that several challenges that seek to reduce agent-regret to a form of guilt fail. I further argue that agent-regret takes as its object not only something one has done, but the fact that one did it; I discuss this in terms of what Bernard Williams called taking an “external” view on one’s own action. -/- I suggest that we can best understand the object of agent-regret as one’s responsibility for an outcome. I argue that this form of “responsibility” is conceptually separate from liability or answerability; it concerns whether the outcome can be ascribed to an agent. This is a restricted form of causal responsibility but retains its agential character. I suggest that we can be responsible for outcomes even when we did not intend to bring them about. -/- In the second part, I vindicate the propriety of agent-regret against the ideas that we are not responsible for unintended outcomes or that such responsibility is not important. I set out several challenges to this effect. I argue that we are responsible for unintended outcomes because in order to be responsible as agents at all, we must use fallible abilities. When we exercise these abilities but fail, we are responsible as agents for those unintended outcomes that arise. I then consider the importance of being responsible for particular unintended outcomes and analyse the idea that this affects our identities. I argue that responsibility for an outcome affects a form of identity, but that it does not involve essential features of a person. Instead, our responsibility for outcomes is a contingent feature that nonetheless plays an important role in our interpersonal interactions and self-conceptions. I argue that these reactions are appropriate, because our responsibility for particular outcomes is independently significant—but these reactions also lend this responsibility added significance as part of inescapable human practices. -/- Thus our responsibility for outcomes is important. Its importance means that it can serve as an appropriate object of agent-regret that vindicates the propriety of agent-regret. I end by considering several interesting features of agent-regret, including its expression and “pure” cases, which are cases where an agent feels agent-regret despite not regretting the result of her action. (shrink)

The authoress shows a simple way to avoid paradoxical consequences of the Czerniawski's argument.

In the recent years we can observe a sort of renaissance of the philosophy of mathematics. More and more papers and books are published. A few years ago a new journal (Philosophia Mathematica) devoted exclusively to the philosophy of mathematics started appearing. In the contemporary discussions - especially in the context of the question of the applicability of mathematics to the description of the physical world - the issue of the existence and the ontological status of mathematical objects plays a (...) particular role. Many new conceptions have appeared - both realistic and antirealistic. In the paper one of the antirealistic conceptions formulated in the recent years is presented - namely a conception by C. Chihara [1990]. The author rejects both Gödel's and Quine's arguments for the realistic standpoint. First, these standpoints will be briefly summarised, since they play a significant role in the contemporary philosophy of mathematics - and are particularly important in the context of the discussion upon Chihara's conception. Next, Chihara's arguments will be analysed in detail. As a result it will turn out that these arguments are not conclusive. Chihara's system relies on certain unjustified assumptions. Moreover, the philosophical difficulties that it encounters are not sufficiently discussed. (shrink)

This article consists of the two parts: the first on presents Hartry Field's nominalistic theory of science contained in his „Science Without Numbers”. The second part points to certain difficulties, which the realization of Field's program is faced with. The problem of an exact translation of nominalistic theories to mathematical theories, the connection between the incompleteness of the nominalistic theory and the conservativeness of its mathematical extension and an example of a theorem about finite sets, which needs some strong assumptions (...) about infinite sets in its proof are presented. (shrink)

In the article the problem of independence in mathematics is discussed. The status of the continuum hypothesis, large cardinal axioms and the axiom of constructablility is presented in some detail. The problem whether incompleteness is really relevant for ordinary mathematics and for empirical science is investigated. Another aim of the article is to give some arguments for the thesis that the problem of reliability and justification of new axioms is well-posed and worthy of attention. In my opinion, investigations concerning the (...) status of independent sentences give insight into our understanding of mathematical concepts, of mathematical knowledge and of the role of mathematics in empirical science. (shrink)