One of the Bell's assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the in uence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell's inequality was derived in its traditional form, without resorting to the hypothesis (...) of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell's inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPR-B nonlocality postulate.We show that the correlations of the observables involved in the Bohm{Bell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality in canonical notatons reads <AB>+<A′B>+<AB′>-<A′B′>≤6. (shrink)

This book is devoted to the presentation of the new quantum mechanical formalism based on the probability representation of quantum states. In the 20s and 30s it became evident that some properties in quantum mechanics can be assigned only to the quantum mechanical system, but not necessarily to its constituents. This led Einstein, Podolsky and Rosen (EPR) to their remarkable 1935 paper where they concluded that quantum mechanics is not a complete theory of nature (EPR paradox). In order to (...) avoid the contradiction which arises from instantaneous action at a distance mentioned above we introduce an extension of the canonical relativity by using measure algebra of physical events in Minkowski space-time. The canonical QM formalism is extended by additional new postulate of EPRB nonlocality for continuous and discrete observables, chapter I. The postulate of EPRB nonlocality is supported by new quantum mechanical formalism based on the probability representation of quantum states. Chapter II is devoted to the new quantum mechanical formalism based on the probability representation of quantum states. Chapter III is devoted to the Einstein's 1927 gedanken experiment resolution. Chapter IV is devoted to the EPR paradox resolution. Chapter V is devoted to the EPR-B paradox resolution. Chapter VI is devoted to the Schrödinger's cat (measured spin) paradox resolution. Chapter VII is devoted to the Bell inequalities revisited. Remind that the canonical arguments which were presented by many authors, namely, that violations of Bell type inequalities signal us that the classical Kolmogorovian model of probability is inapplicable to quantum phenomena. We claimed that the canonical assumption, under which Bell type inequalities were derived, is not supported by real physical nature of the EPRB experiments. The fundamental physical nature violations of the canonical Bell type inequalities explained by Postulate of EPR-Nonlocality and Heisenberg noise-disturbance uncertainty relations. (shrink)

You may not know me well enough to evaluate me in terms of my moral character, but I take it you believe I can be evaluated: it sounds strange to say that I am indeterminate, neither good nor bad nor intermediate. Yet I argue that the claim that most people are indeterminate is the conclusion of a sound argument—the indeterminacy paradox—with two premises: (1) most people are fragmented (they would behave deplorably in many and admirably in many other situations); (...) (2) fragmentation entails indeterminacy. I support (1) by examining psychological experiments in which most participants behave deplorably (e.g., by maltreating “prisoners” in a simulated prison) or admirably (e.g., by intervening in a simulated theft). I support (2) by arguing that, according to certain plausible conceptions, character evaluations presuppose behavioral consistency (lack of fragmentation). Possible reactions to the paradox include: (a) denying that the experiments are relevant to character; (b) upholding conceptions according to which character evaluations do not presuppose consistency; (c) granting that most people are indeterminate and explaining why it appears otherwise. I defend (c) against (a) and (b). (shrink)

If time travel is possible, presumably so is my shooting my younger self ; then apparently I can kill him – I can commit retrosuicide. But if I were to kill him I would not exist to shoot him, so how can I kill him? The standard solution to this paradox understands ability as compossibility with the relevant facts and points to an equivocation about which facts are relevant: my killing YS is compossible with his proximity but not with (...) his survival, so I can kill him if facts like his survival are irrelevant but I cannot if they are relevant. I identify a lacuna in this solution, namely its reliance without argument on the hidden assumption that my killing YS is possible: if it is impossible, it is not compossible with anything. I argue that this lacuna is important, and I sketch a different solution to the paradox. (shrink)

According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians. Introduction (...) Hempel's paradox, the standard Bayesian solution, and the disputed assumption Attempts to defend the disputed assumption Attempts to refute the disputed assumption A way out for Bayesians Conclusion. (shrink)

According to QBism, quantum states, unitary evolutions, and measurement operators are all understood as personal judgments of the agent using the formalism. Meanwhile, quantum measurement outcomes are understood as the personal experiences of the same agent. Wigner’s conundrum of the friend, in which two agents ostensibly have different accounts of whether or not there is a measurement outcome, thus poses no paradox for QBism. Indeed the resolution of Wigner’s original thought experiment was central to the development of QBist thinking. (...) The focus of this paper concerns two very instructive modifications to Wigner’s puzzle: One, a recent no-go theorem by Frauchiger and Renner, and the other a thought experiment by Baumann and Brukner. We show that the paradoxical features emphasized in these works disappear once both friend and Wigner are understood as agents on an equal footing with regard to their individual uses of quantum theory. Wigner’s action on his friend then becomes, from the friend’s perspective, an action the friend takes on Wigner. Our analysis rests on a kind of quantum Copernican principle: When two agents take actions on each other, each agent has a dual role as a physical system for the other agent. No user of quantum theory is more privileged than any other. In contrast to the sentiment of Wigner’s original paper, neither agent should be considered as in “suspended animation.” In this light, QBism brings an entirely new perspective to understanding Wigner’s friend thought experiments. (shrink)

An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.

The “staccato run,” in which a runner stops infinitely often while running from one point to another, is a prototypical “superfeat,” that is, a feat involving the completion in a finite time of an infinite sequence of distinct acts. There is no widely accepted demonstration that superfeats are impossible logically, but I argue here, contra Grunbaüm, that they are impossible dynamically. Specifically, I show that the staccato run is excluded by Newton’s three laws of motion, when those laws are supplemented (...) with a defensible philosophical judgment. (shrink)

In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided (...) within his philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege’s extant logical system, if Frege’s system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege’s logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therein. (shrink)

If you relish paradoxes, this is the book for you. The writings quoted are full of them; the book is largely about “a category beyond all categories”, “atemporal temporality”, “the radical possibility of the impossible itself”, the “concept without concept”, “the myth of the myth, the metaphor of the metaphor”, “hospitality-without-hospitality, brotherhood-without-brotherhood, messianicity-without-messianism”, “relation without relation”, “ethics beyond ethics”, and “the One plus or minus One, no longer exactly One, or more than One”. The author and his protagonists seem to (...) conceive of God only as “wholly other”; nothing constructive can be said about God except perhaps that the wholly other really isn’t wholly other because it is wholly-other-than-other. (shrink)

The history of gender challenges faced by women in elite sports is fraught with controversy and injustice. These athletes' unique physical beauty creates what appears to be a paradox yet is, in fact, scientifically predictable. Intense training for the highest levels of competition leads to unique bodily strength and rare beauty associated with specific anatomic changes, leading top athletes to be singled out as exceptions from their gender and even excluded from competing. Authorities like the IOC and IAF, as (...) well as coaches and fellow athletes, use traditional and sometimes racialized aesthetic norms as the basis for ungrounded judgments of "gender mis-identity." Misjudging the gender identity of elite athletes exemplifies a biased cognitive framework, a form of erroneous and damaging categorical perception that we call "perceptual sexism." We argue that perceptual sexism has a long history within aesthetic and competitive realms and is still perpetuated by popular culture. Correcting this will reduce injustices created by gender identity controversies. (shrink)

This paper tries to reconstruct Ernst Cassirer's potential reception of the EPR argument, as exposed by Einstein in his letter to Cassirer of March 1937. It is shown that, in conformity with his transcendental epistemology taking the conditions of accessibility as constitutive of the quantum object, Cassirer would probably have rejected the argument. Indeed, Cassirer would probably not have subscribed to its separability/local causality presupposition (which goes against his interpretation of the quantum formalism as a self-suf!cient condition constitutive of the (...) quantum object, without any reliance on spatial intuition), nor to its completeness requirement (as his partial endorsement of Bohr's complementarity, and his rejection of the Kantian "idea of complete determination", illustrate). By rejecting both of its premises, Cassirer's philosophy of physics thus enables to escape the EPR dilemma, and exhibits what, in Kantian terms, might be called a "negative utility" with respect to physical science. A further investigation of the anti-reductionist utility of Cassirer's systematic philosophy with respect to physics and other "symbolic forms" is !nally suggested. (shrink)

The paper argues that on three out of eight possible hypotheses about the EPR experiment we can construct novel and realistic decision problems on which (a) Causal Decision Theory and Evidential Decision Theory conflict (b) Causal Decision Theory and the EPR statistics conflict. We infer that anyone who fully accepts any of these three hypotheses has strong reasons to reject Causal Decision Theory. Finally, we extend the original construction to show that anyone who gives any of the three hypotheses any (...) non-zero credence has strong reasons to reject Causal Decision Theory. However, we concede that no version of the Many Worlds Interpretation (Vaidman, in Zalta, E.N. (ed.), Stanford Encyclopaedia of Philosophy 2014) gives rise to the conflicts that we point out. (shrink)

We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...) C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)

In this article, the concept of moralistic fallacy introduced by B. D. Davis is elaborated on in more detail. The main features of this fallacy are discussed, and its general form is presented. The moralistic fallacy might have some undesirable outcomes. Some of them might even be in direct conflict to the original moral position. If this occurs, it is possible to characterize it as a paradox of moralistic fallacy. The possibility of this paradox provides a further reason (...) not to prevent any scientific inquiries and not to depict any knowledge as dangerous. (shrink)

Alternate Universes: Religion assumes the other world after death: paradise, hell, nirvana, karma.. Our world is incomplete, because there is truer universe, replicating Plato: behind something is something.. till the true idea - last judgment, karma.. R. Descartes's "I think, therefore I am", is independent of Plato. I'm thinking, regardless of there is truer idea or not. As I'm thinking, I can realize my first idea was false (eg. solving a math problem), and then the Plato's truer idea reappears. Plato (...) and Descartes precede each other as chicken and egg.. Paradox of Religion: Religions' rules (e.g. don't lie) increase chances of future paradise. Hume's: "A" preceding "B" doesn't need to cause "B" turns to: Expectation of "B" can cause "A" NOW Believers expect paradise to forever delay it. Paradise can paradoxically occur only by deviation from the religion... Exhibited in Holland Park, W8 6LU, The Ice House between 18. Oct - 3. Nov. 2013. (shrink)

McTaggart’s paradox and his A-theory and B-theory are basic notions in the contemporary philosophy of time. It is well known that the paradox was introduced by McTaggart’s paper called “The Unreality of Time” published in 1908, so that it has a one-hundred-year history. As for A-theory and B-theory, in contrast, McTaggart himself didn’t consider both of them at all. The notions of A-theory and B-theory came much later, 60 years after the paradox. Moreover, they had not been (...) as popularized as they are today until quite recently, at least after the 1990s. This paper aims to trace the origin of the notions of A-theory and B-theory and show how the debates behind them, especially objections to “spatialising time,” form the notions. (shrink)

Wittgenstein formulates the paradox of gestalt switches thus: ‘What is incomprehensible is that nothing, and yet everything has changed, after all. That is the only way to put it’. In the course of isolating what I take to be the best of the various solutions to the paradox explored by Wittgenstein, the following claims are defended: (a) A significant strand in Wittgenstein’s own formulation of, and solution to, the paradox can best be understood as a response to (...) three specific claims made by the Gestalt psychologist Kohler. (b) The most promising avenue Wittgenstein explored in his many attempts to resolve the paradox gives perceptual attention a constitutive role in the solution (c) This role is best elaborated, partially, by appeal to information processing theories of attention. (d) There are good reasons to think that the kind of solution to the paradox this yields would have been welcomed by Wittgenstein. (shrink)

In a recent paper in this journal, McCall and Lowe (2003) argue that an understanding of Special Relativity reveals that the A theorist’s notion of temporal passage is consistent with the B theory of time. They arrive at this conclusion by considering the twins’ paradox, where one of two twins (T) travels to Alpha Centauri and back and upon her return has aged 30 years, while her earth-bound twin (S) has aged 40 years. This paper argues that their account (...) of temporal passage fails to reconcile the A theoretic notion of temporal passage with the B theory of time since the B theorist is at liberty to adopt this as an account of temporal passage as understood by the B theorist. (shrink)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to consider (...) the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. These, provides a new interpretation of Quantum Mechanics.More exactly what we see here is "Particle-Fuzzy time" interpretation of quantum Mechanics, in contrast to some other interpretations of Quantum Mechanics like " Wave-Particle" interpretation. At the end, we propound a question about the possible solution of a paradox in Physics, the contradiction between General Relativity and Quantum Mechanics. (shrink)

Deontological ethicists generally agree that there is a way of harming others such that it is wrong to harm others in that way for the sake of producing a comparable but greater benefit for others. Given plausible assumptions about this type of harm, this principle yields the paradoxical result that it may be wrong to do A, wrong to do B, but permissible to do (A and B).

We provide a 'verisimilitudinarian' analysis of the well-known Linda paradox or conjunction fallacy, i.e., the fact that most people judge the probability of the conjunctive statement "Linda is a bank teller and is active in the feminist movement" (B & F) as more probable than the isolated statement "Linda is a bank teller" (B), contrary to an uncontroversial principle of probability theory. The basic idea is that experimental participants may judge B & F a better hypothesis about Linda as (...) compared to B because they evaluate B & F as more verisimilar than B. In fact, the hypothesis "feminist bank teller", while less likely to be true than "bank teller", may well be a better approximation to the truth about Linda. (shrink)

This article critically examines McTaggart’s Paradox, which argues for the unreality of time based on inherent contradictions in the A-series and B-series of temporal order. McTaggart’s assertion that time is unreal stems from the premise that genuine change, essential for time, occurs within the A-series, where events transition from future to present to past. He contends that this series is inherently contradictory, as it requires events to simultaneously possess mutually exclusive properties of past, present, and future. This paradoxical nature (...) leads McTaggart to conclude that time is an illusion. The article challenges McTaggart’s conclusions by advocating for Presentism, the view that only the present moment exists. Presentism is supported by common-sense views and phenomenological experiences of time, which emphasize the experiential privilege of the present. By focusing on the reality of the present moment, Presentism offers a coherent and intuitive understanding of temporal experience, countering McTaggart’s paradox. Additionally, the article explores arguments from philosophers such as Sydney Shoemaker and William Rowe, who challenge McTaggart’s linkage of time with change. Shoemaker proposes that time can exist without change, while Rowe critiques the necessity of change for the existence of time. Through a comprehensive evaluation of McTaggart’s premises and the phenomenological evidence supporting Presentism, this article aims to refute the paradox and affirm the reality of time as experienced through the ever-present ‘Presentness.’ Presentism is thus presented as a robust framework for understanding time, consistent with both philosophical reasoning and everyday temporal experience. (shrink)

On page 14 of "Reconceptions in Philosophy and Other Arts and Sciences" (section 4 of chapter 1) by Nelson Goodman and Catherine Z. Elgin is written: “Since ‘blue’ and ‘green’ are interdefinable with ‘grue’ and ‘bleen’, the question of which pair is basic and which pair derived is entirely a question of which pair we start with”. This paper points out that an example of interdefinability is also that one about the predicate “grueb”, which is a predicate that applies to (...) an object if the object either is green and examined before time b, or is non-green and not examined before time b. The three predicates “green”, “grueb”, “examined before time b” are interdefinable. According to Goodman, since the predicates “blue” and “green” are interdefinable with the predicates “grue” and “bleen”, “if we can tell which objects are blue and which objects are green, we can tell which ones are grue and which ones are bleen” [pages 12-13 of “Reconceptions in Philosophy and Other Arts and Sciences”]. But , even though the predicates “green” and “examined before time b” are interdefinable, being able to tell if an object is green does not imply being able to tell if an object is examined before time b. The interdefinability among three elements is a type of interdefinability present, for example, also among the logical connectives. Another example of interdefinability is that one about a decidable predicate PD, which is interdefinable with an undecidable predicate PU: therefore even though we can tell whether an object is PD and whether an object is non-PD, we cannot tell whether an object is PU (since PU is an undecidable predicate) and whether an object is non-PU. Although the predicates PD and PU are interdefinable, the possibility to determine whether an object is PD does not imply the possibility to determine whether an object is PU (since PU is an undecidable predicate). Similarly, although the predicates “green” and “grue” are interdefinable, the possibility to determine whether an object is “green” even in absence of temporal information does not imply the possibility to determine whether an object is “grue” even in absence of temporal information. These and other examples about “grue” and “bleen” point out that even in case two predicates are interdefinable, the possibility to apply a predicate P does not imply the possibility to apply a predicate interdefinable with P. And that the possibility to apply the predicate “green” without having temporal information does not imply the possibility to apply the predicate “grue” without having temporal information. According to Goodman, if it is possible to determine if an object is green without needing temporal information, then it is also possible to determine if an object is grue without needing temporal information. But, knowing that an object is both green and grue implies temporal information: in fact, we know by definition that a grue object can only be: 1) either green (in case the object is examined before time t); 2) or blue (in case the object is not examined before time t). Thus, knowing that an object is both grue and green, we know that we are faced with case 1, the case of a grue object that is green and examined before time t. Then the paper points out why the Goodman-Kripke paradox is a paradox about meaning that cannot have repercussions on induction. Finally the paper points out why Hume’s problem is a problem different from Goodman’s paradox and requires a specific treatment. (shrink)

Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to consider (...) the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. (shrink)

DEFINING OUR TERMS A “paradox" is an argumentation that appears to deduce a conclusion believed to be false from premises believed to be true. An “inconsistency proof for a theory" is an argumentation that actually deduces a negation of a theorem of the theory from premises that are all theorems of the theory. An “indirect proof of the negation of a hypothesis" is an argumentation that actually deduces a conclusion known to be false from the hypothesis alone or, more (...) commonly, from the hypothesis augmented by a set of premises known to be true. A “direct proof of a hypothesis" is an argumentation that actually deduces the hypothesis itself from premises known to be true. Since `appears', `believes' and `knows' all make elliptical reference to a participant, it is clear that `paradox', `indirect proof' and `direct proof' are all participant-relative. PARTICIPANT RELATIVITY In normal mathematical writing the participant is presumed to be “the community of mathematicians" or some more or less well-defined subcommunity and, therefore, omission of explicit reference to the participant is often warranted. However, in historical, critical, or philosophical writing focused on emerging branches of mathematics such omission often invites confusion. One and the same argumentation has been a paradox for one mathematician, an inconsistency proof for another, and an indirect proof to a third. One and the same argumentation-text can appear to one mathematician to express an indirect proof while appearing to another mathematician to express a direct proof. WHAT IS A PARADOX’S SOLUTION? Of the above four sorts of argumentation only the paradox invites “solution" or “resolution", and ordinarily this is to be accomplished either by discovering a logical fallacy in the “reasoning" of the argumentation or by discovering that the conclusion is not really false or by discovering that one of the premises is not really true. Resolution of a paradox by a participant amounts to reclassifying a formerly paradoxical argumentation either as a “fallacy", as a direct proof of its conclusion, as an indirect proof of the negation of one of its premises, as an inconsistency proof, or as something else depending on the participant's state of knowledge or belief. This illustrates why an argumentation which is a paradox to a given mathematician at a given time may well not be a paradox to the same mathematician at a later time. -/- The present article considers several set-theoretic argumentations that appeared in the period 1903-1908. The year 1903 saw the publication of B. Russell's Principles of mathematics, [Cambridge Univ. Press, Cambridge, 1903; Jbuch 34, 62]. The year 1908 saw the publication of Russell's article on type theory as well as Ernst Zermelo's two watershed articles on the axiom of choice and the foundations of set theory. The argumentations discussed concern “the largest cardinal", “the largest ordinal", the well-ordering principle, “the well-ordering of the continuum", denumerability of ordinals and denumerability of reals. The article shows that these argumentations were variously classified by various mathematicians and that the surrounding atmosphere was one of confusion and misunderstanding, partly as a result of failure to make or to heed distinctions similar to those made above. The article implies that historians have made the situation worse by not observing or not analysing the nature of the confusion. -/- RECOMMENDATION This well-written and well-documented article exemplifies the fact that clarification of history can be achieved through articulation of distinctions that had not been articulated (or were not being heeded) at the time. The article presupposes extensive knowledge of the history of mathematics, of mathematics itself (especially set theory) and of philosophy. It is therefore not to be recommended for casual reading. AFTERWORD: This review was written at the same time Corcoran was writing his signature “Argumentations and logic”[249] that covers much of the same ground in much more detail. https://www.academia.edu/14089432/Argumentations_and_Logic . (shrink)

This paper attempts to provide a clearer formulation of the paradox presented by Annette B. Weiner, in terms of a requirement to keep certain objects within a social group and also a requirement to exchange them with another social group.

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

In the first of the Insolubles in Chapter 8 of his Sophismata, Buridan contends that the inference Omnis propositio est affirmativa; ergo, nulla propositio est negativa (PS) is valid, even though it appeals to the self-reference in the conclusion to show that what we (following Read 2001) call the classical conception of validity (CCV) fails. This requires that we accept that there are good inferences in which a false conclusion follows from true premises. Partially following Hughes’ proposal (1982), we argue (...) that the First Sophism (PS) involves three different notions of validity. Two of them correspond to the ones described by Hughes (1982, 80–86), who calls them Theory A and Theory B. The third one—that will we call Theory C—is not mentioned by Hughes; instead, it is suggested by Buridan himself in the first three arguments in favor of the validity of PS. We show that: a) from what Buridan says in his Theory C it follows that PS is a formal and material consequence, and hence, a valid one. Then we show that: b) the rejection of CCV and the acceptance of Nulla propositio est negativa (NPN) as a (formal) consequence of Omnis propositio est affirmativa (OPA) leads to a paradox that bears similarities with the one put forward by Pseudo Scotus—which has been studied by Read (2001) and is related to Curry’s paradox. However, there are enough differences to merit considering this paradox separately, especially in relation to the so-called validity paradoxes. Interestingly, our work suggests that Buridan was aware of these problems, which explains why he introduced a new criterion for validity, one that is not based on truth-preservation but on what Spade (1988) calls firmness, and Klima (2016) correspondence. (shrink)

In this tour-de-force, Elvira Basevich examines this paradox by tracing the development of W.E.B. Du Bois's life and thought and the relevance of his legacy to our troubled age. She adroitly analyzes the main concepts that inform Du Bois’s critique of American democracy, such as the color line and double consciousness, before examining how these concepts might inform our understanding of contemporary struggles, from Black Lives Matter to the campaign for reparations for slavery. She stresses the continuity in Du (...) Bois’s thought, from his early writings to his later embrace of self-segregation and Pan-Africanism, while not shying away from assessing the challenging implications of his later work.This wonderful book vindicates the power of Du Bois’s thought to help transform a stubbornly unjust world. It is essential reading for racial justice activists as well as students of African American philosophy and political thought. (shrink)

In 1942 Haskell B. Curry presented what is now called Curry's paradox which can be found in a logic independently of its stand on negation. In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this article the non-classical resolution of Curry’s Paradox and Shaw-Kwei' sparadox without rejection any contraction postulate is proposed. In additional relevant paraconsistent logic C ̌_n^#,1≤n<ω, in fact,provide an effective way of circumventing triviality of da Costa’s paraconsistent (...) Set Theories〖NF〗n^C. (shrink)

Peter Godfrey-Smith writes in the section 3.3 “The Ravens Problem” of his book “Theory and Reality” [chapter “Induction and Confirmation”]: “First, the logical empiricists were concerned to deal with the case where generalizations cover an infinite number of instances. In that case, as we see each raven we are not reducing the number of ways in which the hypothesis might fail”. Infinite sets and finite sets have different properties and follow different rules. For example: let’s call “bag X” a specific (...) bag that contains 90 marbles; the generalization A “All marbles in bag X are red” covers a finite number of instances. By contrast, the generalization AE “All things that are not red are not marbles in bag X” covers an infinite number of instances. The propositions A and AE are logically equivalent, but there is an asymmetry due to the fact that A can only have a finite number of instances (since the set of the marbles contained in bag X is a finite set). Because of the aforementioned asymmetry, even though A and AE are logically equivalent propositions, it is wrong to equate an instance of A with an instance of AE. Another example involving a finite set: let’s call “barrique X” a certain 205-liter (54.1553 US gal) barrique. In the following generalization, the expression "all minerals" should not be understood as "all types of minerals", but should be understood literally as "all minerals". B “All minerals are in barrique X”. BE “All objects that are not in barrique X are not minerals”. Of course, a 205-litre barrique cannot contain an infinite number of minerals; the set of objects contained in barrique X is a finite set: therefore in the generalization B we refer to a set that is assumed to be an infinite set (the set of minerals) and to a set (the finite set of minerals contained in barrique X) that is not assumed to be an infinite set. By contrast, in the generalization BE we refer to two sets that are assumed to be infinite sets (the set of all objects that are not contained in barrique X and the set of all objects that are not minerals). Therefore, although B and BE are logically equivalent propositions, an instance of BE cannot be equivalent to an instance of B. Now, let’s analyze the following generalizations. C “All the elements of the set of ravens are elements of the set of black ravens”. CE “All the things that are not elements of the set of black ravens are not elements of the set of ravens”. It is assumed that the number of ravens is infinite, but it is not assumed that the number of black ravens is infinite: that the number of black ravens is infinite is only a hypothesis (for which confirmation is sought), it cannot be assumed as true that the number of black ravens is infinite. Therefore, in the generalization C we refer to a set that is assumed to be an infinite set (the set of ravens) and to a set (the set of black ravens) that is not assumed to be an infinite set. By contrast, in the generalization CE we refer to two sets that are assumed to be infinite sets (the set of all objects that are not elements of the set of black ravens and the set of all objects that are not elements of the set of ravens). Someone could argue that in the generalizations C “All the elements of the set of ravens are elements of the set of black ravens” and CE “All the things that are not elements of the set of black ravens are not elements of the set of ravens” only the set of ravens is assumed to be infinite: but even in this case an asymmetry would remain because C “ All the elements of the set of ravens are elements of the set of black ravens” refers to a set (the set of ravens) that is assumed to be an infinite set and to a set (the set of black ravens) that is not assumed to be infinite; by contrast, CE “All the things that are not elements of the set of black ravens are not elements of the set of ravens” in this case would refer to two sets that are not assumed to be infinite sets. Because of the aforementioned asymmetries, an instance of C cannot be equivalent to an instance of CE. -/- -/- . (shrink)

When we compare the influences of two causes on an outcome, if the conclusion from every group is against that from the conflation, we think there is Simpson’s Paradox. The Existing Causal Inference Theory (ECIT) can make the overall conclusion consistent with the grouping conclusion by removing the confounder’s influence to eliminate the paradox. The ECIT uses relative risk difference Pd = max(0, (R − 1)/R) (R denotes the risk ratio) as the probability of causation. In contrast, Philosopher (...) Fitelson uses confirmation measure D (posterior probability minus prior probability) to measure the strength of causation. Fitelson concludes that from the perspective of Bayesian confirmation, we should directly accept the overall conclusion without considering the paradox. The author proposed a Bayesian confirmation measure b* similar to Pd before. To overcome the contradiction between the ECIT and Bayesian confirmation, the author uses the semantic information method with the minimum cross-entropy criterion to deduce causal confirmation measure Cc = (R − 1)/max(R, 1). Cc is like Pd but has normalizing property (between −1 and 1) and cause symmetry. It especially fits cases where a cause restrains an outcome, such as the COVID-19 vaccine controlling the infection. Some examples (about kidney stone treatments and COVID-19) reveal that Pd and Cc are more reasonable than D; Cc is more useful than Pd. (shrink)

I offer an interpretation and a partial defense of Kit Fine's ‘Argument from Passage’, which is situated within his reconstruction of McTaggart's paradox. Fine argues that existing A-theoretic approaches to passage are no more dynamic, i.e. capture passage no better, than the B-theory. I argue that this comparative claim is correct. Our intuitive picture of passage, which inclines us towards A-theories, suggests more than coherent A-theories can deliver. In Finean terms, the picture requires not only Realism about tensed facts, (...) but also Neutrality, i.e. the tensed facts not being ‘oriented towards’ one privileged time. However unlike Fine, and unlike others who advance McTaggartian arguments, I take McTaggart's paradox to indicate neither the need for a more dynamic theory of passage nor that time does not pass. A more dynamic theory is not to be had: Fine's ‘non-standard realism’ amounts to no more than a conceptual gesture. But instead of concluding that time does not pass, we should conclude that theories of passage cannot deliver the dynamicity of our intuitive picture. For this reason, a B-theoretic account of passage that simply identifies passage with the succession of times is a serious contender. (shrink)

I sitt berömda bevis för tidens overklighet påstod McTaggart att det sätt händelser tycks skifta position i tiden från framtid till nutid och till förfluten tid, innebär en motsägelse. Vad McTaggart egentligen menade har varit föremål för en livlig debatt ända sedan beviset först publicerades 1908. Beviset består av två delar. I den första argumenterar McTaggart för att ingenting kan förändras förutom genom att övergå från framtid till förfluten tid. I den andra argumenterar han för att en sådan övergång innebär (...) en motsägelse och att det därför inte kan finnas någon förändring överhuvudtaget, vilket i sin tur innebär att det heller inte finns någon tid. De flesta filosofer är i dag eniga om att McTaggart har fel, men oeniga om på vilket sätt han har fel. Olika filosofer förkastar olika delar av beviset, beroende på om de har vad som kallas en A- eller B-uppfattning av tiden. De som har en A-uppfattning förnekar att tid förstådd som övergång från framtid till förfluten tid är motsägelsefull. De som har en B-uppfattning förnekar att en övergång från framtid till förfluten tid är nödvändig för förändring, men håller med om att sådan övergång är motsägelsefull. Det är min uppfattning att denna oenighet beror på att McTaggarts argument från första början blivit missuppfattat, av både A- och B-teoretiker. Av någon anledning har det alltid betraktats som ett självständigt argument, ett som är oberoende av det ontologiska system McTaggart förespråkade. Jag föreslår ett nytt sätt att förstå hur han menade att tiden är motsägelsefull. Ett sätt som tar hans ontologiska system som utgångspunkt. (shrink)

In his "Ontological proof", Kurt Gödel introduces the notion of a second-order value property, the positive property P. The second axiom of the proof states that for any property φ: If φ is positive, its negation is not positive, and vice versa. I put forward that this concept of positiveness leads into a paradox when we apply it to the following self-reflexive sentences: (A) The truth value of A is not positive; (B) The truth value of B is positive. (...) Given axiom 2, sentences A and B paradoxically cannot be both true or both false, and it is also impossible that one of the sentences is true whereas the other is false. (shrink)

I point out a sign mistake in the GHZ variant of Bell's theorem, invalidating the GHZ's claim that the premisses of the EPR argument are inconsistent for systems of more than two particles in entangled quantum states.

Two physical "paradoxes" (the paradox of twins in special relativity and that of Einstein, Podolsky, and Rosen in quantum mechanics) are considered philosophically from a common viwepoint. Its essence is the unification of "measurement" and "motion". an idea for the generalization of the concept of reference fram is suggested.

Ignited by Einstein and Bohr a century ago, the philosophical struggle about Reality is yet unfinished, with no signs of a swift resolution. Despite vast technological progress fueled by the iconic Einstein/Podolsky/Rosen paper (EPR) [1] [2] [3], the intricate link between ontic and epistemic aspects of Quantum Theory (QT) has greatly hindered our grip on Reality and further progress in physical theory. Fallacies concealed by tortuous logical negations made EPR comprehension much harder than it could have been had Einstein written (...) it himself in German. EPR is plagued with preconceptions about what a physical property is, the 'Uncertainty Principle', and the Principle of Locality. Numerous interpretations of QT vis à vis Reality exist and are keenly disputed [4] [5] [6] [7] [8] [9] [10] [11]. This is the first of a series of articles arguing for a novel physical interpretation I call ‘The Ontic Probability Interpretation’ (TOPI). A gradual explanation of TOPI is given intertwined with a meticulous logico-philosophical scrutiny of EPR, with Part I focusing on the meaning of Einstein’s ‘incompleteness’ claim for QT: a conceptual confusion, a preconception about Reality, and a flawed dichotomy are shown to be severe obstacles for the EPR argument to succeed. Part II completes the analysis, proving EPR claim of ‘incompleteness’ for QT is fallacious [12]. Part III further develops TOPI, while scrutinizing the mythical ‘Schrödinger’s Cat’, as well as the ‘Basis’ and ‘Measurement’ pseudo-problems [13]. Part IV introduces QR/TOPI: a new theory that solves the century-old problem of integrating Special Relativity with Quantum Theory [14]. (shrink)

After identifying in Part I [1] a conceptual confusion (TCC), a Reality preconception (TRP1), and a fallacious dichotomy (TFD), the famous EPR/EPRB [2] [3] [4] [5] [6] argument for correlated ‘particles’ is now studied in the light of the Ontic Probability Interpretation of Quantum Theory (QT/TOPI). Another Reality preconception (TRP2) is found, showing that EPR used and ignored QT predictions in a single paralogism. Employing TFD and TRP2, EPR unveiled a contradiction veiled in its premises. By removing nonlocality from QT’s (...) Ontology [1] by fiat, EPR preordained its incompleteness. The Petitio Principii fallacy was at work from the outset. Einstein surmised the proper solution to his incompleteness/nonlocality dilemma in 1949 [7], but never abandoned his philosophical stance [8]. It is concluded that there are no definitions of Reality: we have to accept that Reality may not conform to our prejudices and, if an otherwise successful theory predicts what we do not believe in, no gedankenexperiment will help because our biases may slither through. Only actual experiments could assist in solving Einstein’s dilemma, as has been proven in the last 50 years. Notwithstanding, EPR is one of the most influential papers in history and has immensely sparked both conceptual and technological progress. Part III of this series further develops QT/TOPI, while scrutinizing the mythical ‘Schrödinger’s Cat’, as well as the ‘Basis’ and ‘Measurement’ pseudo-problems [9]. Part IV introduces QR/TOPI: a new theory that solves the century-old problem of integrating Special Relativity with Quantum Theory [10]. (shrink)

We present a formal semantics for epistemic logic, capturing the notion of knowability relative to information (KRI). Like Dretske, we move from the platitude that what an agent can know depends on her (empirical) information. We treat operators of the form K_AB (‘B is knowable on the basis of information A’) as variably strict quantifiers over worlds with a topic- or aboutness- preservation constraint. Variable strictness models the non-monotonicity of knowledge acquisition while allowing knowledge to be intrinsically stable. Aboutness-preservation models (...) the topic-sensitivity of information, allowing us to invalidate controversial forms of epistemic closure while validating less controversial ones. Thus, unlike the standard modal framework for epistemic logic, KRI accommodates plausible approaches to the Kripke-Harman dogmatism paradox, which bear on non-monotonicity, or on topic-sensitivity. KRI also strikes a better balance between agent idealization and a non-trivial logic of knowledge ascriptions. (shrink)

This is the first book in a two-volume series. The present volume introduces the basics of the conceptual foundations of quantum physics. It appeared first as a series of video lectures on the online learning platform Udemy.]There is probably no science that is as confusing as quantum theory. There's so much misleading information on the subject that for most people it is very difficult to separate science facts from pseudoscience. The goal of this book is to make you able to (...) separate facts from fiction with a comprehensive introduction to the scientific principles of a complex topic in which meaning and interpretation never cease to puzzle and surprise. An A-Z guide which is neither too advanced nor oversimplified to the weirdness and paradoxes of quantum physics explained from the first principles to modern state-of-the-art experiments and which is complete with figures and graphs that illustrate the deeper meaning of the concepts you are unlikely to find elsewhere. A guide for the autodidact or philosopher of science who is looking for general knowledge about quantum physics at intermediate level furnishing the most rigorous account that an exposition can provide and which only occasionally, in few special chapters, resorts to a mathematical level that goes no further than that of high school. It will save you a ton of time that you would have spent searching elsewhere, trying to piece together a variety of information. The author tried to span an 'arch of knowledge' without giving in to the temptation of taking an excessively one-sided account of the subject. What is this strange thing called quantum physics? What is its impact on our understanding of the world? What is ‘reality’ according to quantum physics? This book addresses these and many other questions through a step-by-step journey. The central mystery of the double-slit experiment and the wave-particle duality, the fuzzy world of Heisenberg's uncertainty principle, the weird Schrödinger's cat paradox, the 'spooky action at a distance' of quantum entanglement, the EPR paradox and much more are explained, without neglecting such main contributors as Planck, Einstein, Bohr, Feynman and others who struggled themselves to come up with the mysterious quantum realm. We also take a look at the experiments conducted in recent decades, such as the surprising "which-way" and "quantum-erasure" experiments. Some considerations on why and how quantum physics suggests a worldview based on philosophical idealism conclude this first volume. This treatise goes, at times, into technical details that demand some effort and therefore requires some basics of high school math (calculus, algebra, trigonometry, elementary statistics). However, the final payoff will be invaluable: Your knowledge of, and grasp on, the subject of the conceptual foundations of quantum physics will be deep, wide, and outstanding. Additionally, because schools, colleges, and universities teach quantum physics using a dry, mostly technical approach which furnishes only superficial insight into its foundations, this manual is recommended for all those students, physicists or philosophers of science who would like to look beyond the mere formal aspect and delve deeper into the meaning and essence of quantum mechanics. The manual is a primer that the public deserves. (shrink)

This article explores some open questions related to the problem of verification of theories in the context of empirical sciences by contrasting three epistemological frameworks. Each of these epistemological frameworks is based on a corresponding central metaphor, namely: (a) Neo-empiricism and the gambling metaphor; (b) Popperian falsificationism and the scientific tribunal metaphor; (c) Cognitive constructivism and the object as eigen-solution metaphor. Each of one of these epistemological frameworks has also historically co-evolved with a certain statistical theory and method for testing (...) scientific hypotheses, respectively: (a) Decision theoretic Bayesian statistics and Bayes factors; (b) Frequentist statistics and p-values; (c) Constructive Bayesian statistics and e-values. This article examines with special care the Zero Probability Paradox (ZPP), related to the verification of sharp or precise hypotheses. Finally, this article makes some remarks on Lakatos’ view of mathematics as a quasi-empirical science. (shrink)

Cognitive scientists claim to have discovered a large number of cognitive biases, which have a tendency to mislead reasoners. Might cognitive scientists themselves be subject to the very biases they purport to discover? And how should this alter the way they evaluate their research as evidence for the existence of these biases? In this paper, we posit a new paradox (the ‘Self-Reflexive Bias Paradox’), which bears a striking resemblance to some classical logical paradoxes. Suppose that research R appears (...) to be good evidence for the existence of bias B, but if B exists, then R would have been subject to B. Thus, it seems sensible for the researcher to reject R as good evidence for the existence of B. However, rejecting R for this reason admits the existence of B. We examine four putative cognitive biases and criticisms of them, each of which seem to be subject to self-reflexivity. In two cases, we argue, paradox is avoidable. In the remaining two, we cannot find a way to avoid the paradox, which poses a practical obstacle to scientific inquiry and results in an intriguing theoretical quandary. (shrink)

The Power Structuralist View (PSV) is an account of causation in which causal relations are reduced to the powers that are activated in the subject by another subject’s power, instantly and simultaneously. PSV is based on two main assumptions: (a) holism; (b) reductionism. After justifying the choice to place PSV within the so-called ‘process accounts’ of causation (PA), I will show how, generally, every PA must solve the so-called “transference paradox” (TP) and why PSV is an innovative account. However, (...) PSV creates two main problems: (1) how to explain the instantaneous activation between correlatives; (2) how to explain which kind of “nexus” takes place between powers. I will argue that, in order to solve (1), PSV needs to adopt an intervalist position, but this leads to a form of monism that contradicts (a). Regarding (2), the reductionist approach implies the assumption that “all relations between powers are internal” and, therefore, a form of monism, again against premise (a). PSV reduces causation to a ‘primitive concept’ (the ontological dependence) but, in this way, point (2) remains unexplained. The problem of physical transference (or reciprocal influence) remains unanswered, and PSV seems to be a covert form of occasionalism. -/- [NOTE: the version on the Journal's site has problems in the footnotes. DOWNLOAD the correct version here in PhilPapers]. (shrink)

With his distinction between the "context of discovery" and the "context of justification", Hans Reichenbach gave the traditional difference between genesis and validity a modern standard formulation. Reichenbach's distinction is one of the well-known ways in which the expression "context" is used in the theory of science. My argument is that Reichenbach's concept is unsuitable and leads to contradictions in the semantic fields of genesis and validity. I would like to demonstrate this by examining the different meanings of Reichenbach's context (...) distinction. My investigation also shows how the difference between genesis and validity precedes Reichenbach's context distinction and indicates approaches for meaningful applications of the concept of context to the phenomena designated by Reichenbach. I will begin by reconstructing the way in which Reichenbach introduces the distinction between discovery and justification as a difference of contexts (I). Drawing on the numerous meanings of the term "context", I will then emphasize some chief characteristics and review, through exemplification, the usage of this term. First of all, I turn to the context of discovery as the nonrational part of all scientific knowledge and show that this meaning cannot be defined consistently (la). For the context of justification, one can distinguish two main cases: the context of justification is either contrasted with the context of discovery, or it forms a unit there with. In the first case, the use of the context term becomes paradoxical, insofar as justification separated from scientific practice does not represent a field of reference which could be specifically contrasted with another field of reference (I b). In the second case, the unifying definitions contradict the contextual meaning of discovery and justification (1 c). In the last section, I point to a useful application of the concept of context which can be found in Reichenbach's argumentation and which refers to the practical conditions of justification(2). (shrink)

In his recent article in Philosophy and Public Affairs, 'The Paradox of Voting and Ethics of Political Representation', Alexander A. Guerrero argues it is rational to vote because each voter should want candidates they support to have the strongest public mandate possible if elected to office, and because every vote contributes to that mandate. The present paper argues that two of Guerrero's premises require correction, and that when those premises are corrected several provocative but compelling conclusions follow about the (...) rationality of voting and duties of elected officials: (A) Voting is typically rational for the members of a political party’s base; (B) Voting is often (but not always) irrational for “swing” voters (i.e. independent voters who are not affiliated with any political party, as well as “undecided” voters who are considering voting across party lines); and (C) Elected officials have a moral duty to respond to changing levels of popular support once in office, as indicated by properly monitored and corroborated public opinion polls of constituents, functioning more as delegates the lower their level of popular support. Finally, I suggest that the last of these conclusions has wide-ranging implications for political ethics. I illustrate these implications by focusing on the questions -- under debate in the 2016 US Presidential election cycle -- of whether a sitting President has a moral duty to nominate or not nominate a new Supreme Court justice during his or her final year in office, and similarly, whether US Senators have a moral duty to obstruct, or not obstruct, confirmation of the President’s eventual nominee. (shrink)

Two strategies to infinity are equally relevant for it is as universal and thus complete as open and thus incomplete. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, thеse phenomena can be elucidated as both complete and incomplete, after which choice is the border between them. A (...) special kind of invariance to the axiom of choice shared by quantum mechanics is discussed to be involved that border between the completeness and incompleteness of infinity in a consistent way. The so-called paradox of Albert Einstein, Boris Podolsky, and Nathan Rosen is interpreted entirely in the same terms only of set theory. Quantum computer can demonstrate especially clearly the privilege of the internal position, or “observer”, or “user” to infinity implied by Henkin’s proposition as the only consistent ones as to infinity. (shrink)

We present an axiomatization of non-relativistic Quantum Mechanics for a system with an arbitrary number of components. The interpretation of our system of axioms is realistic and objective. The EPR paradox and its relation with realism is discussed in this framework. It is shown that there is no contradiction between realism and recent experimental results.

McTaggart’s theory of time is the locus classicus of the contemporary philosophy of time. However, despite its prominence, there is little agreement as to what the theory actually amounts. In this paper, it is first argued that, contrary to the received opinion, McTaggart’s A-time/B-time distinction is not a distinction between static and fluid temporal series. Rather, it is a certain distinction between two types of static temporal series. It is then shown that in his temporal transience paradox, McTaggart employs (...) these two distinct notions of temporal series. The paper is concluded with the claim that McTaggart's temporal transience paradox is best understood not as a contradiction, but as a dilemma both horns of which are unsatisfactory. (shrink)