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)

One of the theories that have been produced in linguistics in the light of J. E. McTaggart’s influential essay “The Unreality of Time” (1908) is a critique of reality that may be attributed to the semantics of tenses in natural languages. This chapter from my book The Linguistic Picture of the World: Alice’s Adventures in Many Languages proposes an alternative approach to the semantics of time, not as a dubious product of linguists’ imagination, i.e. not as something that can easily (...) be discarded from the philosophy of language but rather as a firm category of human thinking. Particular emphasis is placed on the idea of time as it is expressed by the seemingly rather contradictory morphology of the past, present, and future. (shrink)

Recently we proposed "quantum language" (or, the linguistic Copenhagen interpretation of quantum mechanics"), which was not only characterized as the metaphysical and linguistic turn of quantum mechanics but also the linguistic turn of Descartes=Kant epistemology. We believe that quantum language is the language to describe science, which is the final goal of dualistic idealism. Hence there is a reason to want to clarify, from the quantum linguistic point of view, the following problems: "brain in a vat argument", "the Cogito proposition", (...) "five-minute hypothesis", "only the present exists", "Copernican revolution", "McTaggart's paradox", and so on. In this paper, these will be discussed and clarified in quantum language. That is, these are not in quantum language. Also we emphasize that Leibniz's relationalism in Leibniz-Clarke correspondence is regarded as one of the most important parts of the linguistic Copenhagen interpretation of quantum mechanics. This paper is the revised version of the paper: Open Journal of Philosophy, 2018 Vol.8, No.5, 466-480). (shrink)

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)

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)

The intention of this critical review of McTaggart’s 1908 paper is to bring about a distinction between Time and Motion . This distinction is crucial to our understanding of both time as well as motion because so far they have ben treated by all as one and the same. McTaggart, by at least recognizing two different “series” which he calls the A-series and the B-series, has given us a starting point to further understand this distinction. In the process of establishing (...) this distinction we will find ourselves encountering new concepts hitherto unrecognized in philosophy and physics and eventually understand the basis of the numerous paradoxes that time and motion involve dating all the way back to Zeno. (shrink)

McTaggart, in his famous paper, “The Unreality of Time” (1908), argues in favor of the sceptical claim that time is unreal. His main argument is based on detecting a paradox in our ordinary descriptions of time or events occurring in time. Based on our common sense conception of time, time and the events happening in it can be described in two ways: either as having the properties of “being past”, “being present” and “being future”, or as having the properties (...) of “being earlier than”, “being later than”, or “being simultaneous with”. McTaggart argues that employing the second sort of properties fails to properly explain “change” in time. However, having assumed the essentiality of the first type of properties to time, McTaggart argues that these properties will themselves lead to a paradox, according to which all events are at the same time in the past, present, and future. In this essay, we are going to provide a clear exposition of McTaggart’s argument and briefly review some of the main responses to it. We will then show that McTaggart’s argument will amount to error-theory about the content of our utterances about time. We will then employ Boghossian’s argument against error-theory (1990) to show why McTaggart’s argument leads to paradoxical conclusions. (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)

This paper proposes an interpretation of time that is an 'A-theory' in that it incorporates both McTaggart's A-series and his B-series. The A-series characteristics are supposed to be 'ontologically private' analogous to qualia in the problem of other minds and is given a definition. The main idea is that the experimenter and the cat do not share the same A-series characteristics, e.g the same 'now'. So there is no single time at which the cat gets ascribed different states. It (...) is proposed one may define a 'unit of becoming' that coordinatizes the future/present/past 'private' spectrum as well as allowing one to calculate the rates of becoming. Relativity is briefly considered. (shrink)

This paper proposes an interpretation of time that is an 'A-theory' in that it incorporates both McTaggart's A-series and his B-series. The A-series characteristics are supposed to be 'ontologically private' analogous to qualia in the problem of other minds, such as in the Inverted Spectrum thought experiment, and is given a definition. The main idea is then that the experimenter and the cat do not share the same A-series characteristics, e.g. the same 'now', to some extent. So there is (...) no single time at which the cat gets ascribed different states, one by the experimenter and one by the cat. Also it is proposed one may define an ontologically private 'unit of becoming' that coordinatizes the future/present/past A-series spectrum as well as allow one to calculate rates of becoming with seconds. The latter are taken to measure differences in B-series times. (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)

Philosophical views about the logical structure of time are typically divided between proponents of A and B theories, based on McTaggart's A and B series. Drawing on Paul Ricoeur's hermeneutic phenomenology, I develop and defend McTaggart's thesis that the C series and the A series working together give a consistent description of temporal experience, provided that the two series are treated as distinct dimensions internal to time. In the proposed two-dimensional model, the C series expresses a nesting order (...) of the constitutive states of a world, whereas ontological continuity and change are properties of the A series. This, I argue, allows for limited backward causation. (shrink)

Fine’s discussion of McTaggart’s paradox and tense realism may be the most significant progress in the philosophy of time in recent years. Fine reformulates McTaggart’s paradox and develops a novel realist theory called fragmentalism. According to Fine, one major advantage of fragmentalism is its ability to account for the connection between reality and tensed truths. I will argue that fragmentalism cannot give an adequate account of this connection. The reason is that while external relations between fragments are required (...) by this kind of account, these relations are not allowed in fragmentalism. (shrink)

ABSTRACT According to David Lewis, alteration is "qualitative difference between temporal parts of something." It follows that moments, since they are simple and lack temporal parts, cannot alter from future to present to past. Here then is another way to put McTaggart's paradox about change in tense. I will appeal to my theory of Aspects to rebut the thought behind this rendition of McTaggart. On my theory, it is possible that qualitatively differing things be numerically identical. I call (...) these differing, numerically identical things "aspects." I will argue that alteration can be a qualitative difference between temporal aspects of something that lacks temporal parts. So a moment can alter in tense. By rejecting Lewis's assumption my theory can solve this version of McTaggart's paradox. (shrink)

According to Fine’s famous take on the infamous McTaggartian paradox, realism about tensed facts is incompatible with the joint acceptence of three very general and seemingly plausible theses about reality. However, Correia and Rosenkranz have recently objected that Fine’s argument depends on a crucial assumption about the nature of tensed facts; once that assumption is given up, they claim, realists can endorse the theses in question without further ado. They also argue that their novel version of tense realism, called (...) dynamic absolutism, is to be preferred over its rivals. I argue in this paper that dynamic absolutism does not constitute a genuine alternative for realists about tense. (shrink)

There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and (...) logic-based approaches are compared by means of an experiment to show that SP is not basically causal. (shrink)

We shall evaluate two strategies for motivating the view that knowledge is the norm of belief. The first draws on observations concerning belief's aim and the parallels between belief and assertion. The second appeals to observations concerning Moore's Paradox. Neither of these strategies gives us good reason to accept the knowledge account. The considerations offered in support of this account motivate only the weaker account on which truth is the fundamental norm of belief.

There are three questions associated with Simpson’s paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP? and (iii) How to proceed when confronted with SP? An adequate analysis of the paradox starts by distinguishing these three questions. Then, by developing a formal account of SP, and substantiating it with a counterexample to causal accounts, we argue that there are no causal factors at play in answering questions (i) and (ii). Causality enters only in connection with (...) action. (shrink)

We address the need for a model by considering two competing theories regarding the origin of life: (i) the Metabolism First theory, and (ii) the RNA World theory. We discuss two interrelated points, namely: (i) Models are valuable tools for understanding both the processes and intricacies of origin-of-life issues, and (ii) Insights from models also help us to evaluate the core objection to origin-of-life theories, called “the inefficiency objection”, which is commonly raised by proponents of both the Metabolism First theory (...) and the RNA World theory against each other. We use Simpson’s Paradox (SP) as a tool for challenging this objection. We will use models in various senses, ranging from taking them as representations of reality to treating them as theories/accounts that provide heuristics for probing reality. In this paper, we will frequently use models and theories interchangeably. Additionally, we investigate Conway’s Game of Life and contrast it with our SP-based approach to emergence-of-life issues. Finally, we discuss some of the consequences of our view. A scientific model is testable in three senses: (i) a logical sense, (ii) a nomological sense, and (iii) a current technological sense. The SP-based model is testable in the first two senses but it is not feasible to test it using current technology. (shrink)

Fitch’s Paradox shows that if every truth is knowable, then every truth is known. Standard diagnoses identify the factivity/negative infallibility of the knowledge operator and Moorean contradictions as the root source of the result. This paper generalises Fitch’s result to show that such diagnoses are mistaken. In place of factivity/negative infallibility, the weaker assumption of any ‘level-bridging principle’ suffices. A consequence is that the result holds for some logics in which the “Moorean contradiction” commonly thought to underlie the result (...) is in fact consistent. This generalised result improves on the current understanding of Fitch’s result and widens the range of modalities of philosophical interest to which the result might be fruitfully applied. Along the way, we also consider a semantic explanation for Fitch’s result which answers a challenge raised by Kvanvig. (shrink)

I argue that Meno’s Paradox targets the type of knowledge that Socrates has been looking for earlier in the dialogue: knowledge grounded in explanatory definitions. Socrates places strict requirements on definitions and thinks we need these definitions to acquire knowledge. Meno’s challenge uses Socrates’ constraints to argue that we can neither propose definitions nor recognize them. To understand Socrates’ response to the challenge, we need to view Meno’s challenge and Socrates’ response as part of a larger disagreement about the (...) value of inquiry. (shrink)

Since it was presented in 1963, Chisholm’s paradox has attracted constant attention in the deontic logic literature, but without the emergence of any definitive solution. We claim this is due to its having no single solution. The paradox actually presents many challenges to the formalization of deontic statements, including (1) context sensitivity of unconditional oughts, (2) formalizing conditional oughts, and (3) distinguishing generic from nongeneric oughts. Using the practical interpretation of ‘ought’ as a guideline, we propose a linguistically (...) motivated logical solution to each of these problems, and explain the relation of the solution to the problem of contrary-to-duty obligations. (shrink)

If I were to say, “Agnes does not know that it is raining, but it is,” this seems like a perfectly coherent way of describing Agnes’s epistemic position. If I were to add, “And I don’t know if it is, either,” this seems quite strange. In this chapter, we shall look at some statements that seem, in some sense, contradictory, even though it seems that these statements can express propositions that are contingently true or false. Moore thought it was paradoxical (...) that statements that can express true propositions or contingently false propositions should nevertheless seem absurd like this. If we can account for the absurdity, we shall solve Moore’s Paradox. In this chapter, we shall look at Moore’s proposals and more recent discussions of Moorean absurd thought and speech. (shrink)

In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, (...) but not jointly, lack the problematic feature. (shrink)

An examination of McTaggart’s [1908] argument for the unreality of time.

I give an interpretation according to which Meno’s paradox is an epistemic regress problem. The paradox is an argument for skepticism assuming that (1) acquired knowledge about an object X requires prior knowledge about what X is and (2) any knowledge must be acquired. (1) is a principle about having reasons for knowledge and about the epistemic priority of knowledge about what X is. (1) and (2) jointly imply a regress-generating principle which implies that knowledge always requires an (...) infinite sequence of known reasons. Plato’s response to the problem is to accept (1) but reject (2): some knowledge is innate. He argues from this to the conclusion that the soul is immortal. This argument can be understood as a response to an Eleatic problem about the possibility of coming into being that turns on a regress-generating causal principle analogous to the regress-generating principle presupposed by Meno’s paradox. (shrink)

Moore’s Paradox is a test case for any formal theory of belief. In Knowledge and Belief, Hintikka developed a multimodal logic for statements that express sentences containing the epistemic notions of knowledge and belief. His account purports to offer an explanation of the paradox. In this paper I argue that Hintikka’s interpretation of one of the doxastic operators is philosophically problematic and leads to an unnecessarily strong logical system. I offer a weaker alternative that captures in a more (...) accurate way our logical intuitions about the notion of belief without sacrificing the possibility of providing an explanation for problematic cases such as Moore’s Paradox. (shrink)

An important suggestion of objective Bayesians is that the maximum entropy principle can replace a principle which is known to get into paradoxical difficulties: the principle of indifference. No one has previously determined whether the maximum entropy principle is better able to solve Bertrand’s chord paradox than the principle of indifference. In this paper I show that it is not. Additionally, the course of the analysis brings to light a new paradox, a revenge paradox of the chords, (...) that is unique to the maximum entropy principle. (shrink)

This paper argues that justification is accessible in the sense that one has justification to believe a proposition if and only if one has higher-order justification to believe that one has justification to believe that proposition. I argue that the accessibility of justification is required for explaining what is wrong with believing Moorean conjunctions of the form, ‘p and I do not have justification to believe that p.’.

Expressivists explain the expression relation which obtains between sincere moral assertion and the conative or affective attitude thereby expressed by appeal to the relation which obtains between sincere assertion and belief. In fact, they often explicitly take the relation between moral assertion and their favored conative or affective attitude to be exactly the same as the relation between assertion and the belief thereby expressed. If this is correct, then we can use the identity of the expression relation in the two (...) cases to test the expressivist account as a descriptive or hermeneutic account of moral discourse. I formulate one such test, drawing on a standard explanation of Moore's paradox. I show that if expressivism is correct as a descriptive account of moral discourse, then we should expect versions of Moore's paradox where we explicitly deny that we possess certain affective or conative attitudes. I then argue that the constructions that mirror Moore's paradox are not incoherent. It follows that expressivism is either incorrect as a hermeneutic account of moral discourse or that the expression relation which holds between sincere moral assertion and affective or conative attitudes is not identical to the relation which holds between sincere non-moral assertion and belief. A number of objections are canvassed and rejected. (shrink)

The principle of indifference is supposed to suffice for the rational assignation of probabilities to possibilities. Bertrand advances a probability problem, now known as his paradox, to which the principle is supposed to apply; yet, just because the problem is ill‐posed in a technical sense, applying it leads to a contradiction. Examining an ambiguity in the notion of an ill‐posed problem shows that there are precisely two strategies for resolving the paradox: the distinction strategy and the well‐posing strategy. (...) The main contenders for resolving the paradox, Marinoff and Jaynes, offer solutions which exemplify these two strategies. I show that Marinoff’s attempt at the distinction strategy fails, and I offer a general refutation of this strategy. The situation for the well‐posing strategy is more complex. Careful formulation of the paradox within measure theory shows that one of Bertrand’s original three options can be ruled out but also shows that piecemeal attempts at the well‐posing strategy will not succeed. What is required is an appeal to general principle. I show that Jaynes’s use of such a principle, the symmetry requirement, fails to resolve the paradox; that a notion of metaindifference also fails; and that, while the well‐posing strategy may not be conclusively refutable, there is no reason to think that it can succeed. So the current situation is this. The failure of Marinoff’s and Jaynes’s solutions means that the paradox remains unresolved, and of the only two strategies for resolution, one is refuted and we have no reason to think the other will succeed. Consequently, Bertrand’s paradox continues to stand in refutation of the principle of indifference. (shrink)

Zeno’s paradoxes of motion, allegedly denying motion, have been conceived to reinforce the Parmenidean vision of an immutable world. The aim of this article is to demonstrate that these famous logical paradoxes should be seen instead as paradoxes of immobility. From this new point of view, motion is therefore no longer logically problematic, while immobility is. This is convenient since it is easy to conceive that immobility can actually conceal motion, and thus the proposition “immobility is mere illusion of the (...) senses” is much more credible than the reverse thesis supported by Parmenides. Moreover, this proposition is also supported by modern depiction of material bodies: the existence of a ceaseless random motion of atoms—the ‘thermal agitation’—in the scope of contemporary atomic theory, can offer a rational explanation of this ‘illusion of immobility’. Our new approach to Zeno’s paradoxes therefore leads to presenting the novel concept of ‘impermobility’, which we think is a more adequate description of physical reality. (shrink)

In this paper, I argue that the recent discussion on the time - reversal invariance of classical electrodynamics (see (Albert 2000: ch.1), (Arntzenius 2004), (Earman 2002), (Malament 2004),(Horwich 1987: ch.3)) can be best understood assuming that the disagreement among the various authors is actually a disagreement about the metaphysics of classical electrodynamics. If so, the controversy will not be resolved until we have established which alternative is the most natural. It turns out that we have a paradox, namely that (...) the following three claims are incompatible: the electromagnetic fields are real, classical electrodynamics is time-reversal invariant, and the content of the state of affairs of the world does not depend on whether it belongs to a forward or a backward sequence of states of the world. (shrink)

According to the “paradox of knowability”, the moderate thesis that all truths are knowable – ... – implies the seemingly preposterous claim that all truths are actually known – ... –, i.e. that we are omniscient. If Fitch’s argument were successful, it would amount to a knockdown rebuttal of anti-realism by reductio. In the paper I defend the nowadays rather neglected strategy of intuitionistic revisionism. Employing only intuitionistically acceptable rules of inference, the conclusion of the argument is, firstly, not (...) ..., but .... Secondly, even if there were an intuitionistically acceptable proof of ..., i.e. an argument based on a different set of premises, the conclusion would have to be interpreted in accordance with Heyting semantics, and read in this way, the apparently preposterous conclusion would be true on conceptual grounds and acceptable even from a realist point of view. Fitch’s argument, understood as an immanent critique of verificationism, fails because in a debate dealing with the justification of deduction there can be no interpreted formal language on which realists and anti-realists could agree. Thus, the underlying problem is that a satisfactory solution to the “problem of shared content” is not available. I conclude with some remarks on the proposals by J. Salerno and N. Tennant to reconstruct certain arguments in the debate on anti-realism by establishing aporias. (shrink)

The sentences ‘p but I don’t believe p’ (omissive form) and ‘p but I believe that not-p’ (comissive form) are typical examples of Moore’s paradox. When an agent (sincerely) asserts such sentences under normal circumstances, we consider his statements absurd. The Simple Solution (Moore, Heal, Wolgast, Kriegel, et al.) finds the source of absurdity for such statements in a certain formal contradiction (some kind of like ‘p & not-p’), the presence of which is lexically disguised. This solution is facing (...) criticism since it is obvious that the denial of the contradiction allegedly hidden in Moore’s paradox will not become an expression of tautology for us. Hintikka offers another solution to Moore’s paradox. In his view, the source of absurdity is the practical inconceivability of the situation, in which the agent would be able to hold mutually incompatible (inconsistent) beliefs. The sentences ‘p but I don’t believe that p’ and ‘p but I believe that not-p’ sound absurd because they express high-ordered beliefs that no rational agent can hold. A belief expressed in the sentence ‘he believes that p’, in order to be available to the agent, must be compatible with the truth of everything the agent believes. The problem with Hintikka’s solution is that it relies on an epistemic principle that does not correspond to our general intuitions about the notion of belief. According to this principle, there must be a close connection between the sentence ‘p but I don’t believe that p’ and the sentence ‘I believe that is the case is that p but I don’t believe that p’. However, it is not difficult to imagine the context for situations when the agent asserts the sentence ‘p but I don’t believe that p’ when s/he believes that p, but in parallel does not hold any high-ordered belief about his/her belief in p. For example, the agent does not recognize oneself in a photograph after a hard plastic surgery, and when one asks him ‘who is this?’ it would not be absurd for him/her to accept the following description of his/her beliefs ‘I believe that {I am me} but I don’t believe that I believe that {I am me}’. Wittgenstein provides an alternative solution based on a descriptive analysis of the grammar of verbs we use to express, attribute, and understand each other’s psychological states. In his view, the everyday practice of using the verb ‘believe’ demonstrates a characteristic asymmetry in the semantic and logical properties of the usage of this verb in the first person. The expression ‘I believe falsely’ has no real meaning since no one can meaningfully say the sentence ‘Now I believe falsely that p’ on their own behalf. Therefore, the genuine source of absurdity is associated with situations of self-attribution of false belief by the agent. Despite its originality, Wittgenstein’s solution faces objections. For example, in a certain context, it would not be absurd to assert the sentence ‘There are no beliefs, but I don’t believe in it’, unlike the sentence ‘There are no beliefs and I believe that it is so’. The solution proposed by Wittgenstein does not allow us to correct the situation since one could assert quite reasonably and without any absurdity a sentence like ‘In fact, there are no beliefs and now I falsely believe that it is so’. Based on Evans’ principle of epistemic transparency, some researchers (Atlas, Chan, Kwon, et al.) offer another strategy for solving Moore’s paradox, in which peculiar attention is paid to the dependence of understanding and evaluating the meaning of the sentences ‘p but I do not believe that p’ and ‘p but I believe that not-p’ from the immediate context of their usage. The source of absurdity should be looked for in the established practice of the self-referential use of the pronoun ‘I’. In the researchers’ view, Moore’s paradox arises only in the context of situations where the agent asserting such sentences is conscious speaking about oneself. Therefore, there is an obvious structural analogy between the sentences of the Liar family (‘This very sentence is false’, ‘Now I am lying’, etc.) and Moore’s paradox (‘p but I don’t believe that p’, ‘p but I believe that not-p’) – self-reference is constitutive for both families of paradoxical statements. (shrink)

More on McTaggart's AB-series in physics, with integrals.

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)

McTaggart has an insight that changes of property rely on changes of tense (McTaggart 1908). As I show in this paper, he fails to define A-series as a series for changes of tense, and therefore his proof for the unreality of time is unsuccessful. A-series found in the proof is reduced to a number of mere indexicals of time, and this reduction is pushed forward in Dummett's defense. My aim in this paper is not only to check the validity of (...) their arguments but to investigate invincible difficulties faced in defining changes of tense. The latter is my main aim, and the former is a preliminary argument for it. (shrink)

The Russell's paradox concerns the foundations of naive set theory. This short short paper is about how it can be interpreted in other contexts and has significance in the world of commands. Understanding the paper assumes that the reader is broadly familiar with the foundations of set theory and its history. The text contains many formulas and therefore the reader should be comfortable in the world of logical formulas. My example is somewhat similar to the barber paradox. There, (...) too, we are puzzled by the feasibility of a task. In the case of the barber paradox there is a solution: the barber is a woman, in my example there is no such escape. (shrink)

Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same (...) time, the philosophy of probability has been left out. In particular, left out entirely are the philosophical ground of the principle of indifference, the nature of the principle itself, the stringent constraint this places on the mathematical representation of the principle needed for its application to continuum sized event spaces, and what these entail for rigour in developing the paradox itself. This book puts the philosophy and its entailments back in and in so doing casts a new light on the paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it and what the paradox proves for the philosophy of probability. The book finishes with the author’s proposed solution—a solution in the spirit of Bertrand’s, indeed—in which an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference. (shrink)

Unlike almost all other philosophers of science, Karl Popper sought to contribute to natural philosophy or cosmology – a synthesis of science and philosophy. I consider his contributions to the philosophy of science and quantum theory in this light. There is, however, a paradox. Popper’s most famous contribution – his principle of demarcation – in driving a wedge between science and metaphysics, serves to undermine the very thing he professes to love: natural philosophy. I argue that Popper’s philosophy of (...) science is, in this respect, defective. Science cannot proceed without making highly problematic metaphysical assumptions concerning the comprehensibility and knowability of the universe. Precisely because these assumptions are problematic, rigour requires that they be subjected to sustained critical scrutiny, as an integral part of science itself. Popper’s principle of demarcation must be rejected. Metaphysics and philosophy of science become a vital part of science. Natural philosophy is reborn. A solution to the problem of what it means to say a theory is unified is proposed, a problem Popper failed to solve. In The Logic of Scientific Discovery, Popper made important contributions to the interpretation of quantum theory, especially in connection with Heisenberg's uncertainty relations. Popper's advocacy of natural philosophy has important implications for education. (shrink)

If we want to say that all truths are knowable Fitch’s Paradox leads us to conclude that all truths are known. Is it a real philosophical problem or a mere modeling problem? Is it possible to express the idea of knowability using modal logic? The Knowability Principle is expressed by the formula: if Phi is true then it is possible to know that Phi. But what is the meaning of possibility in this context? Using standard modal operators under what (...) condition can we express the idea of knowability? We will in particular examine the subjacent relations of the modal operators in a Kripke Model. We will define the possibility as the possibility of learning opposed to an unclear possibility. Then we will show that Fitch’s Paradox becomes clearer and we will examine how the Knowability Principle could be expressed in such frame. (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)

Weisberg introduces a phenomenon he terms perceptual undermining. He argues that it poses a problem for Jeffrey conditionalization, and Bayesian epistemology in general. This is Weisberg’s paradox. Weisberg argues that perceptual undermining also poses a problem for ranking theory and for Dempster-Shafer theory. In this note I argue that perceptual undermining does not pose a problem for any of these theories: for true conditionalizers Weisberg’s paradox is a false alarm.

It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what (...) was perceived by classical philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the co-incidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato’s Theory of Forms and Aristotle’s metaphysics and logic. Plato’s and Aristotle’s systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a ‘principle of contradiction’ is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing “space” as the seat of stability, and “time” as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion ‘separable system’, related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of ‘non-locality’ as related to it, indicating the need to re-think the notions system, entity, as well as the implications of the operation ‘measurement’, which is seen here as an application of classical logic (including its ontological consequences) on the material world. (shrink)

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

Philosophy of science is seen by most as a meta-discipline – one that takes science as its subject matter, and seeks to acquire knowledge and understanding about science without in any way affecting, or contributing to, science itself. Karl Popper’s approach is very different. His first love is natural philosophy or, as he would put it, cosmology. This intermingles cosmology and the rest of natural science with epistemology, methodology and metaphysics. Paradoxically, however, one of his best known contributions, his proposed (...) solution to the problem of demarcation, helps to maintain the gulf that separates science from metaphysics, thus fragmenting cosmology into falsifiable science on the one hand, untestable philosophy on the other. This has damaging repercussions for a number of issues Popper tackles, from the problem of induction to simplicity of theory and quantum theory. But his proposed solution to the demarcation problem is untenable. Metaphysical assumptions are an integral part of scientific knowledge, inherent in the persistent acceptance of unified theories against the evidence. Once this is appreciated, it becomes obvious that natural philosophy, a synthesis of science and philosophy, is both more rigorous and of greater intellectual value than the two dissociated components we have today. What Popper sought for could come to full fruition. Problems that Popper tackled, from the problem of induction, to the problem of unity of theory, problems of quantum theory, and problems concerning the scope and limits of physics, all receive more adequate resolution within the new, fully-fledged natural philosophy. (shrink)

I consider a puzzling case presented by Jose Benardete, and by appeal to this case develop a paradox involving counterfactual conditionals. I then show that this paradox may be leveraged to argue for certain non-obvious claims concerning the logic of counterfactuals.

John Turri gives an example that he thinks refutes what he takes to be “G. E. Moore's view” that omissive assertions such as “It is raining but I do not believe that it is raining” are “inherently ‘absurd'”. This is that of Ellie, an eliminativist who makes such assertions. Turri thinks that these are perfectly reasonable and not even absurd. Nor does she seem irrational if the sincerity of her assertion requires her to believe its content. A commissive counterpart of (...) Ellie is Di, a dialetheist who asserts or believes that The Russell set includes itself but I believe that it is not the case that the Russell set includes itself. Since any adequate explanation of Moore's paradox must handle commissive assertions and beliefs as well as omissive ones, it must deal with Di as well as engage Ellie. I give such an explanation. I argue that neither Ellie's assertion nor her belief is irrational yet both are absurd. Likewise neither Di's assertion nor her belief is irrational yet in contrast neither is absurd. I conclude that not all Moore-paradoxical assertions or beliefs are irrational and that the syntax of Moore's examples is not sufficient for the absurdity found in them. (shrink)

The model-theoretic argument known as Putnam´s paradox threatens our notion of truth with triviality: Almost any world can satisfy almost any theory. Formal argument and intuition are at odds. David Lewis devised a solution according to which the very stucture of the world fixes how it is to be divided into elite classes which determine the reference of any true theory. Three claims are defended: Firstly, Lewis´ proposal must be completed by an account of successful referential intentions. Secondly, contrary (...) to Catherine Elgin´s criticism of Lewis, natural properties corresponding to elite classes may play a role in sound scientific inquiry. Thirdly, despite Bas van Fraassen´s objection that the sceptic cannot consistently maintain doubts about reference, there is a promising sceptical strategy of exploiting Putnam´s results which is answered by Lewis´ account. (shrink)