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)

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.’.

Is self-knowledge a requirement of rationality, like consistency, or means-ends coherence? Many claim so, citing the evident impropriety of asserting, and the alleged irrationality of believing, Moore-paradoxical propositions of the form < p, but I don't believe that p>. If there were nothing irrational about failing to know one's own beliefs, they claim, then there would be nothing irrational about Moore-paradoxical assertions or beliefs. This article considers a few ways the data surrounding Moore's paradox might be (...) marshaled to support rational requirements to know one's beliefs, and finds that none succeed. (shrink)

In this article, I consider the cases of religious Moorean propositions of the form ‘d, but I don't believe that d’ and ‘d, but I believe that ~d’, where d is a religious dogma, proposition, or part of a creed. I argue that such propositions can be genuinely and rationally asserted and that this fact poses a problem for traditional analysis of religious assertion as an expression of faith and of religious faith as entailing belief. In the article, (...) I explore the possibility of undermining these commonly held assumptions and argue that the assertability of religious Moorean propositions can be justified by an account of faith as an intention to form religious beliefs. In the end, I also consider the consequences of such a stance, especially concerning the debate on the ethics of religious belief and doxastic voluntarism. (shrink)

In this paper I will compare two competing accounts of assertion: the knowledge account and the justified belief account. When it comes to the evidence that is typically used to assess accounts of assertion – including the evidence from lottery propositions, the evidence from Moore’s paradoxical propositions and the evidence from conversational patterns – I will argue that the justified belief account has at least as much explanatory power as its rival. I will argue, finally, that a (...) close look at the ways in which assertions can be challenged and retracted reveals a certain advantage for the justified belief account. The paper will touch upon a number of further topics along the way, including the logical interaction between knowledge and justified belief, the nature of defeat, and the hypothesis that knowledge and justified belief are normatively coincident goals. (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.

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)

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)

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)

Nico Silins (2012, 2013, 2020) argues that conscious judgments justify self-attribution of belief in the content judged. In defending his view, he makes use of Moore’s Paradox, seeking to show how his theory can explain what seems irrational or absurd about sentences of the form, ‘p and I do not believe that p’. I show why his argument strategy is not available to defend the view that conscious judgments can justify the self-attribution of belief in the content judged. I then (...) propose an amended version of his theory, which holds that sincerely asserting a proposition—whether aloud or silently—justifies self-ascribing belief in the proposition expressed. In doing so, I draw on an argument which I made in Gregory (2018) that there is something it is like to make a sincere assertion which is different from what it is like to make an insincere assertion. The phenomenology of sincere assertion provides immediate justification for self-ascription of belief in a proposition which has been sincerely asserted; nonetheless, it may be that we need to interpret our own assertions in order to determine which propositions they express. This paves the way for showing how two competing schools of thought about self-knowledge—one which holds that self-knowledge is immediate and one which holds that self-knowledge is inferential—might be combined. (shrink)

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)

Moore’s paradox, the infamous felt bizarreness of sincerely uttering something of the form “I believe grass is green, but it ain’t”—has attracted a lot of attention since its original discovery (Moore 1942). It is often taken to be a paradox of belief—in the sense that the locus of the inconsistency is the beliefs of someone who so sincerely utters. This claim has been labeled as the priority thesis: If you have an explanation of why a putative content could not be (...) coherently believed, you thereby have an explanation of why it cannot be coherently asserted. (Shoemaker 1995). The priority thesis, however, is insufficient to give a general explanation of Moore-paradoxical phenomena and, moreover, it’s false. I demonstrate this, then show how to give a commitment-theoretic account of Moore Paradoxicality, drawing on work by Bach and Harnish. The resulting account has the virtue of explaining not only cases of pragmatic incoherence involving assertions, but also cases of cognate incoherence arising for other speech acts, such as promising, guaranteeing, ordering, and the like. (shrink)

Phenomenal conservatives claim that seemings are sui generis mental states and can thus provide foundational non-doxastic justification for beliefs. Many of their critics deny this, claiming, instead, that seemings can be reductively analyzed in terms of other mental states—either beliefs, inclinations to believe, or beliefs about one’s evidence—that cannot provide foundational non-doxastic justification. In this paper, I argue that no tenable semantic reduction of ‘seems’ can be formulated in terms of the three reductive analyses that have been proposed by critics (...) of phenomenal conservatism. This is because Moore-paradoxical statements are generated when each of the reductive analyses is substituted for ‘seems’ in statements like ‘The stick is straight, but it does not seem to me that it’s straight.’ Since the latter statement is not Moore-paradoxical, the three proposed reductive analyses of ‘seems’ are unsuccessful. Absent a successful semantic reduction, however, there is no good reason to think a successful metaphysical reduction of seemings is forthcoming. Thus, there is an additional reason, unnoticed in the existing literature, to think that seemings are sui generis mental states. (shrink)

I give an account of the absurdity of Moorean beliefs of the omissive form(om) p and I don’t believe that p,and the commissive form(com) p and I believe that not-p,from which I extract a definition of Moorean absurdity. I then argue for an account of the absurdity of Moorean assertion. After neutralizing two objections to my whole account, I show that Roy Sorensen’s own account of the absurdity of his ‘iterated cases’(om1) p and I don’t believe that I believe that (...) p,and(com1) p and I believe that I believe that not-p,is unsatisfactory. I explain why it is less absurd to believe or assert (om1) or (com1) than to believe or assert (om) or (com) and show that despite appearances, subsequent iterations of (om1) or (com1) do not decrease the absurdity of believing or asserting them. (shrink)

The aim of this paper is to argue that what I call the simple theory of introspection can be extended to account for our introspective knowledge of what we believe as well as what we consciously experience. In section one, I present the simple theory of introspection and motivate the extension from experience to belief. In section two, I argue that extending the simple theory provides a solution to Moore’s paradox by explaining why believing Moorean conjunctions always involves some degree (...) of irrationality. In section three, I argue that it also solves the puzzle of transparency by explaining why it’s rational to answer the question whether one believes that p by answering the question whether p. Finally, in section four, I defend the simple theory against objections by arguing that self-knowledge constitutes an ideal of rationality. (shrink)

We present counterexamples to the widespread assumption that Moorean sentences cannot be rationally asserted. We then explain why Moorean assertions of the sort we discuss do not incur the irrationality charge. Our argument involves an appeal to the dual-process theory of the mind and a contrast between the conditions for ascribing beliefs to oneself and the conditions for making assertions about independently existing states of affairs. We conclude by contrasting beliefs of the sort we discuss with the structurally similar but (...) rationally impermissible beliefs of certain psychiatric patients. (shrink)

A speaker's use of a declarative sentence in a context has two effects: it expresses a proposition and represents the speaker as knowing that proposition. This essay is about how to explain the second effect. The standard explanation is act-based. A speaker is represented as knowing because their use of the declarative in a context tokens the act-type of assertion and assertions represent knowledge in what's asserted. I propose a semantic explanation on which declaratives covertly host a "know"-parenthetical. A speaker (...) is thereby represented as knowing the proposition expressed because that is the semantic contribution of the parenthetical. I call this view parentheticalism and defend that it better explains knowledge representation than alternatives. As a consequence of outperforming assertoric explanations, parentheticalism opens the door to eliminating the act-type of assertion from linguistic theorizing. (shrink)

In this essay, I develop an account of belief as commitment to the truth of a proposition. On my account, to believe p is to represent p as true by way of committing to the truth of p. To commit to the truth of p, in the sense I am interested in, is to exercise the normative power to subject one’s representation of p as true to the normative standard of truth. As I argue, my account of belief as commitment (...) of the truth explains a variety of features of belief that separate it from attitudes like acceptance, supposition, and imagination. Most importantly, it explains the distinctive connection between belief and evidence. Moreover, my account helps solve three further puzzles about belief, regarding doxastic voluntarism, the aim of belief, and Moore’s paradox. (shrink)

This paper argues that to account for group speech acts, we should adopt a representationalist account of mode / force. Individual and collective subjects do not only represent what they e.g. assert or order. By asserting or ordering they also indicate their theoretical or practical positions towards what they assert or order. The ‘Frege point’ cannot establish the received dichotomy of force and propositional content. On the contrary, only the representationalist account allows a satisfactory response to it. It also allows (...) us to give a more satisfactory analysis of the speech act of inviting a joint commitment and to answer two important questions Bernhard Schmid has raised about group speech acts, namely whether there are 1st person plural forms of Moore’s paradox and of 1st person authority. (shrink)

Certain combinations of attitudes are manifestly unreasonable. It is unreasonable to believe that dogs bark, for example, if one concedes that one has no justification to believe this. Why are the irrational combinations irrational? One suggestion is that these are attitudes that a subject cannot have justification to have. If this is right, we can test claims about the structure of propositional justification by relying on our observations about which combinations of attitudes constitute Moorean absurd pairs. In a recent defense (...) of access internalism, Smithies argues that only access internalism can explain why various combinations of attitude are irrational. In this paper, I shall argue that access internalism cannot explain the relevant data. Reflection on Moore's Paradox will not tell us much of anything about propositional justification and cannot support access internalism. (shrink)

Suppose you’re imagining that it’s raining hard. You then proceed to imagine, as part of the same imaginative project, that you believe that it isn’t raining. Such an imaginative project is possible if the two imaginings arise in succession. But what about simultaneously imagining that it’s raining and that you believe that it isn’t raining? I will argue that, under certain conditions, such an imagining is impossible. After discussing these conditions, I will suggest an explanation of this impossibility. Elaborating on (...) the view outlined in Walton (1990), I will argue that the impossibility follows from the fact that imaginings ‘mimic’ beliefs in aiming at the fictionally true, just as beliefs aim at the true. (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)

Russell discovered the classes version of Russell's Paradox in spring 1901, and the predicates version near the same time. There is a problem, however, in dating the discovery of the propositional functions version. In 1906, Russell claimed he discovered it after May 1903, but this conflicts with the widespread belief that the functions version appears in _The Principles of Mathematics_, finished in late 1902. I argue that Russell's dating was accurate, and that the functions version does not appear in the (...) _Principles_. I distinguish the functions and predicates versions, give a novel reading of the _Principles_, section 85, as a paradox dealing with what Russell calls _assertions_, and show that Russell's logical notation in 1902 had no way of even formulating the functions version. The propositional functions version had its origins in the summer of 1903, soon after Russell's notation had changed in such a way as to make a formulation possible. (shrink)

I argue that the familiar picture of the rise of analytic philosophy through the early work of G. E. Moore and Bertrand Russell is incomplete and to some degree erroneous. Archival evidence suggests that a considerable influence on Moore, especially evident in his 1899 paper ‘The nature of judgment,’ comes from the literature in nineteenth-century empirical psychology rather than nineteenth-century neo-Hegelianism, as is widely believed. I argue that the conceptual influences of Moore’s paper are more likely to have had their (...) source in the work of two of Moore’s teachers, G. F. Stout and James Ward. What may be called an anti-psychologism about psychology characterizes the work of these and other psychologists of the period. I argue that the anti-psychologism that is the main aim of Moore’s early theory of judgment is an adaptation of this notion, which is significantly dissimilar from the notion defended by Bradley, traditionally thought to have been a key influence on Moore.Keywords: G. E. Moore; Bertrand Russell; Propositions; Anti-psychologism; Early analytic philosophy; G. F. Stout. (shrink)

Several interesting themes emerge from G. E. Moore’s previously unpub­lished review of _The Principles of Mathematics_. These include a worry concerning whether mathematical notions are identical to purely logical ones, even if coextensive logical ones exist. Another involves a conception of infinity based on endless series neglected in the Principles but arguably involved in Zeno’s paradox of Achilles and the Tortoise. Moore also questions the scope of Russell’s notion of material implication, and other aspects of Russell’s claim that mathematics reduces (...) to logic. (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 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)

In a recent paper by Tranchini (Topoi, 2019), an introduction rule for the paradoxical proposition ρ∗ that can be simultaneously proven and disproven is discussed. This rule is formalized in Martin-Löf’s constructive type theory (CTT) and supplemented with an inferential explanation in the style of Brouwer-Heyting-Kolmogorov semantics. I will, however, argue that the provided formalization is problematic because what is paradoxical about ρ∗ from the viewpoint of CTT is not its provability, but whether it is a proposition at (...) all. (shrink)

This paper critically examines currently influential transparency accounts of our knowledge of our own beliefs that say that self-ascriptions of belief typically are arrived at by “looking outward” onto the world. For example, one version of the transparency account says that one self-ascribes beliefs via an inference from a premise to the conclusion that one believes that premise. This rule of inference reliably yields accurate self-ascriptions because you cannot infer a conclusion from a premise without believing the premise, and so (...) you cannot infer from a premise that you believe the premise unless you do believe it. I argue that this procedure cannot be a source of justification, however, because one can be justified in inferring from p that q only if p amounts to strong evidence that q is true. This is incompatible with the transparency account because p often is not very strong evidence that you believe that p. For example, unless you are a weather expert, the fact that it will rain is not very strong evidence that you believe it will rain. After showing how this intuitive problem can be made precise, I conclude with a broader lesson about the nature of inferential justification: that beliefs, when justified, must be underwritten by beliefs, when justified, must be underwritten by evidential relationships between the facts or propositions which those beliefs represent. (shrink)

This thesis focuses on expressively rich languages that can formalise talk about probability. These languages have sentences that say something about probabilities of probabilities, but also sentences that say something about the probability of themselves. For example: (π): “The probability of the sentence labelled π is not greater than 1/2.” Such sentences lead to philosophical and technical challenges; but can be useful. For example they bear a close connection to situations where ones confidence in something can affect whether it is (...) the case or not. The motivating interpretation of probability as an agent's degrees of belief will be focused on throughout the thesis. -/- This thesis aims to answer two questions relevant to such frameworks, which correspond to the two parts of the thesis: “How can one develop a formal semantics for this framework?” and “What rational constraints are there on an agent once such expressive frameworks are considered?”. (shrink)

I offer a novel account of the absurdity of Moore-paradoxical assertion in terms of an interlocutor’s fully conscious beliefs. This account starts with an original argument for the principle that fully conscious belief collects over conjunction. The argument is premised on the synchronic unity of consciousness and the transparency of belief.

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)

The Gettier Problem and Moore’s Paradox are related in a way that is unappreciated by philosophers. If one is in a Gettier situation, then one is also in a Moorean situation. The fact that S is in a Gettier situation (the fact that S is “Gettiered”), like the fact that S is in a Moorean situation (the fact that S is “Moored”), cannot (in the logical sense of “cannot”) be known by S while S is in that situation. The paper (...) starts the job of mapping what can be said about this feature of Gettier situations. The goal is to stimulate further exploration into this yet uncharted territory. (shrink)

Hempel’s Converse Consequence Condition (CCC), Entailment Condition (EC), and Special Consequence Condition (SCC) have some prima facie plausibility when taken individually. Hempel, though, shows that they have no plausibility when taken together, for together they entail that E confirms H for any propositions E and H. This is “Hempel’s paradox”. It turns out that Hempel’s argument would fail if one or more of CCC, EC, and SCC were modified in terms of explanation. This opens up the possibility that Hempel’s (...) paradox can be solved by modifying one or more of CCC, EC, and SCC in terms of explanation. I explore this possibility by modifying CCC and SCC in terms of explanation and considering whether CCC and SCC so modified are correct. I also relate that possibility to Inference to the Best Explanation. (shrink)

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with (...) other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems). (shrink)

David Kaplan famously argued that mainstream semantics for modal logic, which identifies propositions with sets of possible worlds, is affected by a cardinality paradox. Takashi Yagisawa showed that a variant of the same paradox arises when standard possible worlds semantics is extended with impossible worlds to deliver a hyperintensional account of propositions. After introducing the problem, we discuss two general approaches to a possible solution: giving up on sets and giving up on worlds, either in the background semantic (...) framework or in the corresponding conception of propositions. As a result, we conclude that abandoning worlds by embracing a truthmaker-based approach offers a promising way to account for hyperintensional propositions without facing the paradoxical outcome. (shrink)

Chalmers and Hájek argue that on an epistemic reading of Ramsey’s test for the rational acceptability of conditionals, it is faulty. They claim that applying the test to each of a certain pair of conditionals requires one to think that one is omniscient or infallible, unless one forms irrational Moore-paradoxical beliefs. I show that this claim is false. The epistemic Ramsey test is indeed faulty. Applying it requires that one think of anyone as all-believing and if one is rational, (...) to think of anyone as infallible-if-rational. But this is not because of Moore-paradoxical beliefs. Rather it is because applying the test requires a certain supposition about conscious belief. It is important to understand the nature of this supposition. (shrink)

One of Moore’s paradoxical sentence types is ‘P, but I believe ~P’. Mooreans have assumed that all tokens of that sentence type are absurd in some way: epistemically, pragmatically, semantically, or assertively. And then they proceed to debate what the absurdity really is. I argue that if one has the appropriate philosophical views, then one can rationally assert tokens of that sentence type, and one can be epistemically reasonable in the corresponding compound belief as well.

This paper offers an analysis of a hitherto neglected text on insoluble propositions dating from the late XiVth century and puts it into perspective within the context of the contemporary debate concerning semantic paradoxes. The author of the text is the italian logician Peter of Mantua (d. 1399/1400). The treatise is relevant both from a theoretical and from a historical standpoint. By appealing to a distinction between two senses in which propositions are said to be true, it offers (...) an unusual solution to the paradox, but in a traditional spirit that contrasts a number of trends prevailing in the XiVth century. It also counts as a remarkable piece of evidence for the reconstruction of the reception of English logic in italy, as it is inspired by the views of John Wyclif. Three approaches addressing the Liar paradox (Albert of Saxony, William Heytesbury and a version of strong restrictionism) are first criticised by Peter of Mantua, before he presents his own alternative solution. The latter seems to have a prima facie intuitive justification, but is in fact acceptable only on a very restricted understanding, since its generalisation is subject to the so-called revenge problem. (shrink)

Scientific realists believe both what a scientific theory says about observables and unobservables. In contrast, scientific antirealists believe what a scientific theory says about observables, but not about unobservables. I argue that scientific realism is a more useful doctrine than scientific antirealism in science classrooms. If science teachers are antirealists, they are caught in Moore’s paradox when they help their students grasp the content of a scientific theory, and when they explain a phenomenon in terms of a scientific theory. Teachers (...) ask questions to their students to check whether they have grasped the content of a scientific theory. If the students are antirealists, they are also caught in Moore’s paradox when they respond positively to their teachers’ questions, and when they explain a phenomenon in terms of a scientific theory. Finally, neither teachers nor students can understand phenomena in terms of scientific theories, if they are antirealists. (shrink)

Can I be wrong about my own beliefs? More precisely: Can I falsely believe that I believe that p? I argue that the answer is negative. This runs against what many philosophers and psychologists have traditionally thought and still think. I use a rather new kind of argument, – one that is based on considerations about Moore's paradox. It shows that if one believes that one believes that p then one believes that p – even though one can believe (...) that p without believing that one believes that p. (shrink)

I discuss what I call practical Moore sentences: sentences like ‘You must close your door, but I don’t know whether you will’, which combine an order together with an avowal of agnosticism about whether the order will be obeyed. I show that practical Moore sentences are generally infelicitous. But this infelicity is surprising: it seems like there should be nothing wrong with giving someone an order while acknowledging that you do not know whether it will obeyed. I suggest that this (...) infelicity points to a striking psychological fact, with potentially broad ramifications concerning the structure of norms of speech acts: namely, when giving an order, we must act as if we believe we will be obeyed. (shrink)

Speaks defends the view that propositions are properties: for example, the proposition that grass is green is the property being such that grass is green. We argue that there is no reason to prefer Speaks's theory to analogous but competing theories that identify propositions with, say, 2-adic relations. This style of argument has recently been deployed by many, including Moore and King, against the view that propositions are n-tuples, and by Caplan and Tillman against King's view that (...) propositions are facts of a special sort. We offer our argument as an objection to the view that propositions are unsaturated relations. (shrink)

Sequel to Part I. In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions and equivalence classes of coextensional properties. Part II addresses Russell’s own various attempts to solve these (...) paradoxes, including strategies that he considered and rejected (limitation of size, the zigzag theory, etc.), as well as his own final views whereupon many purported entities that, if reified, lead to these contradictions, must not be genuine entities, but ‘logical fictions’ or ‘logical constructions’ instead. (shrink)

In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions, and equivalence classes of coextensional properties. Part I focuses on Cantor’s theorem, its proof, how it can be used to (...) manufacture paradoxes, Frege’s diagnosis of the core difficulty, and several broad categories of strategies for offering solutions to these paradoxes. (shrink)

I argue that the accounts of inference recently presented (in this journal) by Paul Boghossian, John Broome, and Crispin Wright are unsatisfactory. I proceed in two steps: First, in Sects. 1 and 2, I argue that we should not accept what Boghossian calls the “Taking Condition on inference” as a condition of adequacy for accounts of inference. I present a different condition of adequacy and argue that it is superior to the one offered by Boghossian. More precisely, I point out (...) that there is an analog of Moore’s Paradox for inference; and I suggest that explaining this phenomenon is a condition of adequacy for accounts of inference. Boghossian’s Taking Condition derives its plausibility from the fact that it apparently explains the analog of Moore’s Paradox. Second, in Sect. 3, I show that neither Boghossian’s, nor Broome’s, nor Wright’s account of inference meets my condition of adequacy. I distinguish two kinds of mistake one is likely to make if one does not focus on my condition of adequacy; and I argue that all three—Boghossian, Broome, and Wright—make at least one of these mistakes. (shrink)

Dellsén (2016a) argues that understanding requires neither justification nor belief. I object that ridding understanding of justification and belief comes with the following costs. (i) No claim about the world can be inferred from what we understand. (ii) We run into either Moore’s paradox or certain disconcerting questions. (iii) Understanding does not represent the world. (iv) Understanding cannot take the central place in epistemology. (v) Understanding cannot be invoked to give an account of scientific progress. (vi) It is not clear (...) how misunderstanding arises. (shrink)

Russell claims in his autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class not be (...) thought of as a single thing, neither can the meaning/intension of any expression capable of singling out one collection (class) of things as opposed to another. If this is right, it shows that Russell’s method of solving the logical paradoxes is wholly incompatible with anything like a Fregean dualism between sense and reference or meaning and denotation. I also discuss how this realization lead to modifications in his understanding of propositions and propositional functions, and suggest that Russell’s confrontation with these issues may be instructive for ongoing research. (shrink)

This paper offers a cheap solution to Laura Valentini’s paradox of ideal theory. An ideal theory cannot be sound by definition, since in the relevant sense of “ideal theory” it involves false propositions.

The present work outlines a logical and philosophical conception of propositions in relation to a group of puzzles that arise by quantifying over them: the Russell-Myhill paradox, the Prior-Kaplan paradox, and Prior's Theorem. I begin by motivating an interpretation of Russell-Myhill as depending on aboutness, which constrains the notion of propositional identity. I discuss two formalizations of of the paradox, showing that it does not depend on the syntax of propositional variables. I then extend to propositions a modal (...) predicative response to the paradoxes articulated by an abstraction principle for propositions. On this conception, propositions are “shadows” of the sentences that express them. Modal operators are used to uncover the implicit relation of dependence that characterizes propositions that are about propositions. The benefits of this approach are shown by application to other intensional puzzles. The resulting view is an alternative to the plenitudinous metaphysics of impredicative comprehension principles. (shrink)