Believing that p, assuming that p, and imagining that p involve regarding p as true—or, as we shall call it, accepting p. What distinguishes belief from the other modes of acceptance? We claim that conceiving of an attitude as a belief, rather than an assumption or an instance of imagining, entails conceiving of it as an acceptance that is regulated for truth, while also applying to it the standard of being correct if and only if it is true. We argue (...) that the second half of this claim, according to which the concept of belief includes a standard of correctness, is required to explain the fact that the deliberative question whether to believe that p is transparent to the question whether p. This argument raises various questions. Is there such a thing as deliberating whether to believe? Is the transparency of the deliberative question whether to believe that p the same as the transparency of the factual question whether I do believe that p? We will begin by answering these questions and then turn to a series of possible objections to our argument. (shrink)

Why, when asking oneself whether to believe that p, must one immediately recognize that this question is settled by, and only by, answering the question whether p is true? Truth is not an optional end for first-personal doxastic deliberation, providing an instrumental or extrinsic reason that an agent may take or leave at will. Otherwise there would be an inferential step between discovering the truth with respect to p and determining whether to believe that p, involving a bridge premise that (...) it is good (in whichever sense of good one likes, moral, prudential, aesthetic, allthings-considered, etc.) to believe the truth with respect to p. But there is no such gap between the two questions within the first-personal deliberative perspective; the question whether to believe that p seems to collapse into the question whether p is true. (shrink)

Two prejudices have hampered our understanding of John Stuart Mill’s central argument for free speech. One prejudice is that arguments for free speech can only be made in terms of values or rights. This prejudice causes us to miss the depth of Mill’s argument. He does not argue that silencing speech is harmful or violates rights, but instead that silencing speech is a uniquely self-undermining act; it undermines the ground upon which it is based. But even if we overcome this (...) prejudice and appreciate the self-undermining character of Mill’s argument, the prejudice that epistemic justification is a completable task blinds us to the role of open-mindedness in his argument; and failing to see this leads us to wrongly conclude that his argument is invalid. It is only once we have overcome both prejudices that we can appreciate the depth and power of Mill’s argument for free speech. (shrink)

When we deliberate whether to believe some proposition, we feel immediately compelled to look for evidence of its truth. Philosophers have labelled this feature of doxastic deliberation 'transparency'. I argue that resolving the disagreement in the ethics of belief between evidentialists and pragmatists turns on the correct explanation of transparency. My hypothesis is that it reflects a conceptual truth about belief: a belief that p is correct if and only if p. This normative truth entails that only evidence can be (...) a reason for belief. Although evidentialism does not follow directly from the mere psychological truth that we cannot believe for non-evidential reasons, it does follow directly from the normative conceptual truth about belief which explains why we cannot do so. (shrink)

Why can't deliberation conclude in an intention except by considering whether to perform the intended action? I argue that the answer to this question entails that reasons for intention are determined by reasons for action. Understanding this feature of practical deliberation thus allows us to solve the toxin puzzle.

We refine the arithmetical hierarchy of various classical principles by finely investigating the derivability relations between these principles over Heyting arithmetic. We mainly investigate some restricted versions of the law of excluded middle, De Morgan's law, the double negation elimination, the collection principle and the constant domain axiom.

As Descartes famously pointed out in theSecond Meditation,the thought that someone is thinking is true anytime anyone thinks it. Furthermore, thinking it makes it true. Conversely, anytime anyone thinks that it is not the case that someone is thinking, this thought is false, and thinking it makes it false.l will argue that the propositions ‘There is at least one true normative proposition’ and ‘There are no true normative propositions’ have very similar properties. The proposition ‘There is at least one true (...) normative proposition,’ like the proposition ‘Someone is thinking,’ is true anytime anyone believes it, and, in an important sense, it is made true by someone's believing it. Conversely, anytime anyone believes that there are no true normative propositions, the proposition he believes is false and his believing it makes it false. (shrink)

It is common for philosophers to claim that doxastic voluntarism, the view that an agent can form beliefs voluntarily, is false, and therefore that agents do not have the kind of control over their beliefs required for a straightforward application of deontological concepts such as obligation or duty in the domain of epistemology. The role that the denial of doxastic voluntarism plays in an argument to the effect that agents do not have obligations with respect to belief is simply this.

Mark Schroeder has recently presented apparent counterexamples to the standard account of the distinction between the right and the wrong kinds of reasons. We argue that these examples appear to refute the standard account only because they blur the distinction between two kinds of reasoning: reasoning about whether to intend or believe that p and reasoning about whether to take up the question of whether to intend or believe that p.

The COVID-19 pandemic has shaken the world. After liberalization in 1991, microfinance became a panacea for poor people without collateral and information asymmetry. The higher cost of microfinance and debt traps highlighted the need for the state to intervene in resource redistribution. In addition, national lockdowns and COVID-19 restrictions have made it difficult for emerging economies like India to achieve this sustainable development goal. The Reserve Bank of India introduced self-help group (SHG) bank linkage to ensure the financial inclusion of (...) the poor. The difference-in-difference method examined how SHGs affect entrepreneur households’ income. CMIE Consumer Pyramid dx data were used for analysis. The data establish that SHGs have increased the income of the households, and demographic factors such as education, income level and gender also impact the financial inclusion of the poor. (shrink)

In this paper, I show that the availability of what some authors have called the weak reading and the strong reading of donkey sentences with relative clauses is systematically related to monotonicity properties of the determiner. The correlation is different from what has been observed in the literature in that it concerns not only right monotonicity, but also left monotonicity (persistence/antipersistence). I claim that the reading selected by a donkey sentence with a double monotone determiner is in fact the one (...) that validates inference based on the left monotonicity of the determiner. This accounts for the lack of strong reading in donkey sentences with MON determiners, which have been neglected in the literature. I consider the relevance of other natural forms of inference as well, but also suggest how monotonicity inference might play a central role in the actual process of interpretation. The formal theory is couched in dynamic predicate logic with generalized quantifiers. (shrink)

Akama et al. [1] introduced a hierarchical classification of first-order formulas for a hierarchical prenex normal form theorem in semi-classical arithmetic. In this paper, we give a justification for the hierarchical classification in a general context of first-order theories. To this end, we first formalize the standard transformation procedure for prenex normalization. Then we show that the classes $$\textrm{E}_k$$ and $$\textrm{U}_k$$ introduced in [1] are exactly the classes induced by $$\Sigma _k$$ and $$\Pi _k$$ respectively via the transformation procedure in (...) any first-order theory. (shrink)

We identify bar recursion on moduli of continuity as a fundamental notion of constructive mathematics. We show that continuous functions from the Baire space \ to the natural numbers \ which have moduli of continuity with bar recursors are exactly those functions induced by Brouwer operations. The connection between Brouwer operations and bar induction allows us to formulate several continuity principles on the Baire space stated in terms of bar recursion on continuous moduli which naturally characterise some variants of bar (...) induction. These principles state that a certain kind of continuous function from \ to \ admits a modulus of continuity with a bar recursor. The results for the Baire space are recast in the setting of the Cantor space \ using the notion of fan recursor, a bar recursor for binary trees. This yields characterisations of uniformly continuous functions on the Cantor space and fan theorem in terms of fan recursors. The results for the Cantor space hold over the extensional version of intuitionistic arithmetic in all finite types ), and those for the Baire space hold over \ extended with the type for Brouwer operations. Our work places Spector’s bar recursion in a proper context of Brouwer’s intuitionistic mathematics and clarifies the connection between bar recursion and bar induction. (shrink)

On sait que Platon fait grand cas des êtres intelligibles en instaurant la théorie des Idées. Mais il n’est pas approprié de le considérer comme penseur qui néglige le rôle de l’apparence sensible. Ce philosophe demeure très sensible à la modalité par laquelle les phénomènes apparaissent dans le champ de notreperception. En distinguant deux types d’apparence : image et simulacre, il donne à l’image le rôle d’intermédiaire actif entre le sensible et l’intelligible. L’examen des modalités des actions humaines qui reçoivent (...) et créent des images, nous aide à voir comment Platon intègre la fonction des images dans la structure de sa philosophie. La réception et la création des images sont étroitement reliées et synthétisées pour former le système original de Platon, système dans lequel le fondement de la théorie des Idées relève d’un certain dynamisme de l’action humaine. Dans la recherche relative à la modalité de réception et de création des images, je porte mon attention sur l’usage platonicien du terme tupos qui exprime le principe de la conformité de l’image et de son modèle.Notamment dans la théorie de la formation des futurs gardiens de la cité idéale, le tupos fonctionne, comme un principe qui réglemente et oriente à plusieurs niveaux les activités de la mimèsis et de la poièsis qui portent sur les images. La réflexion sur cette fonction conductrice. (shrink)

In the past decade, a growing number of authors, notably Thomas Pogge, have maintained that citizens in economically advanced societies are responsible for extreme and extensive poverty in the developing world. Iris Marion Young proposed the social connection model of responsibility, which asserts that these citizens participate in networks that give rise to global structural injustices. While Pogge’s argument for the existence of citizens’ responsibility has been the subject of widespread debate, few efforts have been made to scrutinise the solidity (...) of Young’s perspective. To plug this gap in the literature, this paper assesses the pertinence of Young’s view. A more traditional view than those of Pogge and Young considers poverty as indicating a lack of respect for the human rights of those living in less-developed countries. Rights theorists of global justice, however, have paid scant attention to philosophical observations concerning redistribution within the borders of a society. To remedy this shortcoming, this paper endeavours to develop the theory that citizens in affluent societies bear a duty correlative to the subsistence right of the global needy, by exploring sufficientarianism, which is one of the primary views on domestic redistribution. To begin with, I make a distinction between the responsibility-based theory and the right-based theory of global justice. This is followed by a close examination of Young’s social connection model as a significant version of the former position. I then offer a right-based argument that invokes the sufficientarian idea of the human right to live above the threshold of safe and healthy subsistence. (shrink)

Akama et al. [1] systematically studied an arithmetical hierarchy of the law of excluded middle and related principles in the context of first-order arithmetic. In that paper, they first provide a prenex normal form theorem as a justification of their semi-classical principles restricted to prenex formulas. However, there are some errors in their proof. In this paper, we provide a simple counterexample of their prenex normal form theorem [1, Theorem 2.7], then modify it in an appropriate way which still serves (...) to largely justify the arithmetical hierarchy. In addition, we characterize a variety of prenex normal form theorems by logical principles in the arithmetical hierarchy. The characterization results reveal that our prenex normal form theorems are optimal. For the characterization results, we establish a new conservation theorem on semi-classical arithmetic. The theorem generalizes a well-known fact that classical arithmetic is $\Pi _2$ -conservative over intuitionistic arithmetic. (shrink)

We provide a fine‐grained analysis on the relation between König's lemma, weak König's lemma, and the decidable fan theorem in the context of constructive reverse mathematics. In particular, we show that double negated variants of König's lemma and weak König's lemma are equivalent to double negated variants of the general decidable fan theorem and the binary decidable fan theorem, respectively, over a nearly intuitionistic system containing a weak countable choice only. This implies that the general decidable fan theorem is not (...) equivalent to the binary decidable fan theorem in the absence of a strong countable choice. In addition, we introduce a principle which fills the gap between König's lemma and weak König's lemma, and show that König's lemma is equivalent to weak König's lemma plus this principle. We also solve several problems arising from the investigation. (shrink)

The uniform continuity theorem states that every pointwise continuous real‐valued function on the unit interval is uniformly continuous. In constructive mathematics, is strictly stronger than the decidable fan theorem, but Loeb [17] has shown that the two principles become equivalent by encoding continuous real‐valued functions as type‐one functions. However, the precise relation between such type‐one functions and continuous real‐valued functions (usually described as type‐two objects) has been unknown. In this paper, we introduce an appropriate notion of continuity for a modulus (...) of a continuous real‐valued function on [0, 1], and show that real‐valued functions with continuous moduli are exactly those functions induced by Loeb's codes. Our characterisation relies on two assumptions: (1) real numbers are represented by regular sequences (equivalently Cauchy sequences with explicitly given moduli); (2) the continuity of a modulus is defined with respect to the product metric on the regular sequences inherited from the Baire space. Our result implies that is equivalent to the statement that every pointwise continuous real‐valued function on [0, 1] with a continuous modulus is uniformly continuous. We also show that is equivalent to a similar principle for real‐valued functions on the Cantor space. These results extend Berger's [2] characterisation of for integer‐valued functions on and unify some characterisations of in terms of functions having continuous moduli. (shrink)

George, feeling stressed and anxious about the criminal investigation into his firm’s accounting practices, decides that it would do him good to get away and take a long, relaxing vacation in Bermuda. According to popular informed-desire accounts of a person’s good, if George would desire to take a vacation to Bermuda upon being made fully aware of what his experience of the vacation would be like and of all the consequences therein, then this course of action would benefit him. This (...) does not mean that George must actually be privy to whether his fully informed self would desire to travel to Bermuda, but whether he would, according to such an account, determines whether going to Bermuda would benefit George, whether he or anyone else is capable of knowing it. (shrink)

We systematically study conservation theorems on theories of semi-classical arithmetic, which lie in-between classical arithmetic $\mathsf {PA}$ and intuitionistic arithmetic $\mathsf {HA}$. Using a generalized negative translation, we first provide a structured proof of the fact that $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over $\mathsf {HA} + {\Sigma _k}\text {-}\mathrm {LEM}$ where ${\Sigma _k}\text {-}\mathrm {LEM}$ is the axiom scheme of the law-of-excluded-middle restricted to formulas in $\Sigma _k$. In addition, we show that this conservation theorem is optimal in the (...) sense that for any semi-classical arithmetic T, if $\mathsf {PA}$ is $\Pi _{k+2}$ -conservative over T, then ${T}$ proves ${\Sigma _k}\text {-}\mathrm {LEM}$. In the same manner, we also characterize conservation theorems for other well-studied classes of formulas by fragments of classical axioms or rules. This reveals the entire structure of conservation theorems with respect to the arithmetical hierarchy of classical principles. (shrink)

By using a provability predicate of PA, we define ThmPA(M) as the set of theorems of PA in a modelMof PA. We say a modelMof PA is (1) illusory if ThmPA(M) ⊈ ThmPA(ℕ), (2) heterodox if ThmPA(M) ⊈ TA, (3) sane ifM⊨ ConPA, and insane if it is not sane, (4) maximally sane if it is sane and ThmPA(M) ⊆ ThmPA(N) implies ThmPA(M) = ThmPA(N) for every sane modelNof PA. We firstly show thatMis heterodox if and only if it is (...) illusory, and that ThmPA(M) ∩ TA ≠ ThmPA(ℕ) for any illusory modelM. Then we show that there exists a maximally sane model, every maximally sane model satisfies ¬ConPA+ConPA, and there exists a sane model of ¬ConPA+ConPAwhich is not maximally sane. We define that an insane model is (5) illusory by nature if its every initial segment being a nonstandard model of PA is illusory, and (6) going insane suddenly if its every initial segment being a sane model of PA is not illusory. We show that there exists a model of PA which is illusory by nature, and we prove the existence of a model of PA which is going insane suddenly. (shrink)

Kierstead showed that every computable marriage problem has a computable matching under the assumption of computable expanding Hall condition and computable local finiteness for boys and girls. The strength of the marriage theorem reaches or if computable expanding Hall condition or computable local finiteness for girls is weakened. In contrast, the provability of the marriage theorem is maintained in even if local finiteness for boys is completely removed. Using these conditions, we classify the strength of variants of marriage theorems in (...) the context of reverse mathematics. Furthermore, we introduce another condition that also makes the marriage theorem provable in, and investigate the sequential and Weihrauch strength of marriage theorems under that condition. (shrink)

We aim at developing a systematic method of separating omniscience principles by constructing Kripke models for intuitionistic predicate logic $\mathbf {IQC}$ and first-order arithmetic $\mathbf {HA}$ from a Kripke model for intuitionistic propositional logic $\mathbf {IPC}$. To this end, we introduce the notion of an extended frame, and show that each IPC-Kripke model generates an extended frame. By using the extended frame generated by an IPC-Kripke model, we give a separation theorem of a schema from a set of schemata in (...) $\mathbf {IQC}$ and a separation theorem of a sentence from a set of schemata in $\mathbf {HA}$. We see several examples which give us separations among omniscience principles. (shrink)

Translated text is chapt. 7, pt. 2 of Kirisutokyō no benshō.

We shall prove the second incompleteness theorem via Kolmogorov complexity.

We propose a new game to strategically justify the constrained equal awards rule in claims problems. Our game is “procedurally fair” and “multilateral”. In addition, even if claimants cannot reach an agreement in any period, they can renegotiate in the next period. We show that, for each claims problem, the awards vector chosen by the constrained equal awards rule achieved at period 1 is the unique subgame perfect equilibrium outcome of the game.

We systematically study several principles and give a principle which is weaker than disjunctive Markov’s principle. We also show that the principle is underivable and strictly weaker than MP∨ in certain extensions of the system EL of elementary analysis.

Taylor and Francis Ltd TSEP_A_151217.sgm..

Hajime Tanabe (1885-1962), the Kyoto- School philosopher of modern Japan, attempts to interpret Aristotle's ontology as being involved in the logic of self-identical being without self-negative conversion in action from his own dialectical perspective. For Tanabe, the eternal essence or Form is to be mediated by the dynamic character of matter, i.e., the temporality pertinent to the changing movement. For Aristotle, however, the essence or pure activity as the principle of being is devoid of such a dynamic mediation, but is (...) rather regarded as the past being, i.e., what it should be originally and eternally. In other words, for Aristotle, evil and matter are the lacks of goodness and the eternal Form that are identical with the essence of the individual substance. Evil is to be self-negatively mediated to goodness in free action through conversion in Tanabe's perspective. Movement pertaining to matter is not simply an incompletion of pure activity, but is rather self-negatively converted into the activity as the transcendent principle of the dialectical unification of time and eternity, matter and Form, evil and Goodness. The individual existence has freedom to unify the self-contradistinctive opposed moments, i.e., subjective action and objective being in a way of mutually negating conversion. The difference between Tanabe and Aristotle lies in that for Tanabe practice is relevant to the future, whereas for Aristotle contemplation is concerned with eternity as invariable and imperishable being since the past. While Aristotle's logic is confined to the self-identity of being in contemplation, Tanabe's logic is structured by the triadic elements of individuality, species as the relative universal, and genus as the absolute universal in terms of the negative conversion in action. (shrink)