The general aim of this book is to provide an elementary exposition of some basic concepts in terms of which both classical and non-dassicallogirs may be studied and appraised. Although quantificational logic is dealt with briefly in the last chapter, the discussion is chiefly concemed with propo gjtional cakuli. Still, the subject, as it stands today, cannot br covered in one book of reasonable length. Rather than to try to include in the volume as much as possible, I have put (...) emphasis on some selected topics. Even these could not be roverrd completely, but for each topic I have attempted to present a detailed and precise t’Xposition of several basic results including some which are non-trivial. The roots of some of the central ideas in the volume go back to J. Luka siewicz’s seminar on mathematicallogi. (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)

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.

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)

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)

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.

The article examines the concept of anti-irrationalism coined by the members of the Lvov-Warsaw School. The term “anti-irrationalism” comes from Ajdukiewicz, who used it to define the specificity of the School as a whole. For Ajdukiewicz, anti-irrationalism, which values cognition with intersubjective qualities, is contrasted with irrationalism. The article discusses Twardowski’s tripartite division of beliefs into rational, “irrational,” and “non-rational.” Against this background, the article explores Dąmbska’s view on irrationalism, which is divided by her into several subcategories.Finally, the author considers (...) the question of anti-irrationalism as a metaphilosophical standpoint in the context of the question of a worldview. (shrink)

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)

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)

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)

The paper attempts to reconstruct Thales’ argument about water, which is rightly considered to be the core of his philosophy of nature. It consists of two separate arguments – one biological and the other physical – which ascribe to water two different functions: in the first case, it is a source of life on the earth or, in another version, a source of life of the earth in its entirety; in the second case, it is something that supports the earth (...) in its stationary position in the cosmos. These two arguments indicate that Thales’ notion of water was meant to answer more than just one question about nature. This, in turn, might justify the use of the concept of arche, which Aristotle attributed to the Ionian philosophers, even though Thales had obviously never used the term. The concept may somehow accurately render Thales’ more general view of water. It should be noted, however, that if the term arche can be applied to Thales’ views, then it is only in the sense related to the “coming-to-be”. Thales’ arguments did not apply – contrary to what some doxographers said and what certain scholars still maintain – to the question of the end, or perishing of physical things, the problem taken up only by later Ionians. To put it differently, Thales never claimed that the physical things which die or undergo destruction change into water. (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)

Cooperation between doctors of various specialties and other medical specialists is the standard of care in the treatment of patients. Due to the variety of diseases and the dynamic development of medicine in general, it is difficult to be an expert in every field and know all the recommended treatments. An example of such cooperation is the joint treatment of patients with the problem of ingrown toenails. The article contains an analysis of patients who received treatment in a doctor’s office (...) in cooperation with podiatrists. A conservative approach towards the treatment of this condition sees the patient being initially diagnosed and treated by a podiatrist and then later, if necessary, being referred to a doctor for surgical treatment. The exchange of experiences and information on patients treated by interdisciplinary teams allows doctors and podiatrists to find the best possible treatment and improve the quality of life of patients. The follow-up of patients after surgery can be performed later in podiatry offices. Owing to modern electronic communication, it is possible for a doctor to constantly monitor the patient’s condition without the need for direct visits to the doctor’s office. (shrink)

In this article several metalogical properties which are interesting and important from the philosophical point of view are discussed. Examples of non-classical logical systems which posses these properties are presented.

An Antique Prototype of the Modern Mathematisation of Psychology Ryszard Stachowski. (1) matter or that which is not in itself a particular thing, (2) form or essence, which is that precisely in accordance with which a thing is called a this, and ...

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)

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)

In a departure from traditional Western political theory that is reminiscent of left?wing anarchism, contemporary libertarianism rejects the necessity of making political choices based on a value hierarchy, instead claiming that it is possible for all individuals to pursue their divergent values simultaneously?as long as each respects the equal rights of others to do the same. The caveat, however, hides a conflict of loyalties that would plague a libertarian society: on the one hand are the particular loyalties of one's preferred (...) Utopian community; on the other hand, loyalty to the larger ?framework for utopias?; within which one's utopia exists. The second loyalty implies a value relativism incompatible with the first one, meaning either that loyalty to the libertarian framework will undermine the utopias within it, or that the particular values of the utopias will destabilize the libertarian framework. The durability of a libertarian society, then, requires a mentality best characterized as nihilistic. In this, libertarianism differs from liberalism but is surprisingly similar to the cultural diversity movement. The thesis is illustrated by examining John Gray's attempt to eschew both a hierarchy of values and moral relativism. (shrink)

The two main points of this contribution are the following: (1) Applied mathematical theories might complement physical theories in an essential way; some applied mathematical theories allow us to understand phenomena we are unable to explain by resorting to physical theories alone, (2) In the case of social sciences it might be necessary to account for examined phenomena by resorting to the idea of goal-oriented activity (the causal approach typical for natural science might be unsatisfactory). Weinberg's idea of grand reductionism (...) ignores the two above mentioned facts and hence overestimates the foundational role of physics and its methodology. (shrink)

The difference between what's possible and what's not is a construct of the human mind, a matter of perspective, and it's one that can be changed. Working Wonders explains the fundamentals that shape the mind: how it builds walls to protect itself and how a person can tear those walls down to tackle challenges that would have previously been discounted as unrealistic. This volume shares case studies featuring people making the impossible a reality and, in doing so, changing the world (...) for the better. On a deeper level and yet still using non-technical language, the book identifies possible neurological and psychosocial mechanisms that limit the brain, and techniques that may open it up to exploring the seemingly unachievable. Praszkier also introduces the concept of 'possibilitivity', a personality trait that reflects the propensity to perceive insurmountable challenges as doable, and concludes by presenting a portfolio of 'Do It Yourself' techniques. (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)

11 original. Modifications which I introduced are radical and often far going. In my opinion the Polish text had two main drawbacks. It was overloaded with informal considerations and at the same time formal concepts included in some parts of the book were presented in a too complicated way. Of course one of the motives to revise it was also the fact that much time has passed since I finished writing the Polish version and obviously certain decisions and ideas contained (...) in the first edition seem not quite relevant now. So it is not only the desire to make the exposition clearer but also the reasons of substantial nature which motivated writing a revised version. I do not think it desirable to bother the reader with a detailed discussion of all changes to which the Polish version was subjected and that is why I will confine myself to pointing out only the most significant ones. Explanations concerning logical and set-theoretical notions applied in the book have been shortened as much as possible, in the Polish version one whole chapter was devoted to the discussion of them. (shrink)

Traditional theism (in Christianity, Judaism and Islam) understands God as possessing certain attributes including omnipotence. God is omnipotent in the sense that God possesses unlimited (maximal) power. For some classical philosophers and theologians (PetrusDamiani, René Descartes) God’s omnipotence requires his being able to do absolutely anything, including the logically impossible. But in Thomas Aquinas’ opinion, to do what is logically impossible is not an act of power but is self-contradictory action. For Aquinas, a logically impossible action is not an action. (...) The contemporary British philosopher of religion, Richard Swinburne, considers omnipotence from an analytic perspective and, partially,within Aquinas’ tradition. For Swinburne, omnipotence includes the power to perform only logically possible and consistent tasks. In this paper, I discuss systematically (§§ 3-6) the philosophical and logical problems of omnipotence and the relation between God and logic from the perspective of Jan Łukasiewicz’s logical investigations. Keywords: Omnipotence, God, logic, rationality, Richard Swinburne, Jan Łukasiewicz. (shrink)

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