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Jonathan Haidt is a moral psychologist whose influential book, The Righteous Mind: Why Good People are Divided by Politics and Religion, explains the origins of our political disagreements. The aim of the book is to encourage understanding and civility in our public life. Deliberative democrats also have a significant stake in understanding the sources of our disagreements and see rational deliberation as the key to civility and democratic legitimacy. However, Haidt’s empirical studies give reasons to suggest that the “faith” of deliberative democrats in reasoning may be misplaced, particularly as that faith tends be inflected in terms of a “Kantian” moral psychology.This article analyzes four different explanatory “stories” that Haidt weaves together: (1) a “causal” evolutionary account of the development of morality; (2) a “causal” story about the psychological mechanisms explaining human action; (3) a “causal” story about the historical and cultural determinants of our political attitudes; and (4) a “normative” story about the grounds and justification of human action. The article then examines these stories to discern how deliberative democrats might rearticulate their conception of public reasoning, and their normative hopes for it, in light of Haidt’s findings by introducing the “embedded” conception of public reasoning.

This paper considers the time continuum of Brouwer in terms of the complex system physics. It is based upon a processual definition of real numbers which concern the measurement problem. The multiresolution hierarchy of the measurement process is represented by the time operator acting on continuous signals. The wavelet domain hidden Markov model, which recapitulates statistical properties of the hierarchy, is verified experimentally on a wide range of signal ensembles. It indicates a novel method that has already been proved to be tremendously useful in applied mathematics.

On a bilateralist reading, sequents are interpreted as statements to the effect that, given the assertion of the antecedent it is incoherent to deny the succedent. This interpretation goes against its own ecumenical ambitions, endowing Cut with a meaning very close to that of tertium non datur and thus rendering it intuitionistically unpalatable. This paper explores a top-down route for arguing that, even intuitionistically, a prohibition to deny is as strong as a licence to assert. [ABSTRACT FROM AUTHOR]

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We may try to explain proofs as chains of valid inference, but the concept of validity needed in such an explanation cannot be the traditional one. For an inference to be legitimate in a proof it must have sufficient epistemic power, so that the proof really justifies its final conclusion. However, the epistemic concepts used to account for this power are in their turn usually explained in terms of the concept of proof. To get out of this circle we may consider an idea within intuitionism about what it is to justify the assertion of a proposition. It depends on Heyting's view of the meaning of a proposition, but does not presuppose the concept of inference or of proof as chains of inferences. I discuss this idea and what is required in order to use it for an adequate notion of valid inference. [ABSTRACT FROM AUTHOR]

In his paper "Explaining Deductive Inference" Prawitz states what he calls «a fundamental problem of logic and the philosophy of logic»: the problem of explaining «Why do certain inferences have the epistemic power to confer evidence on the conclusion when applied to premisses for which there is evidence already?». In this paper I suggest a way of articulating, and partly modifying, the intuitionistic answer to this problem in such a way as to both answer Prawitz's problem and satisfy a requirement I argue to be crucial for any epistemic theory of the meaning of the logical constants: the requirement that evidence is epistemically transparent. [ABSTRACT FROM AUTHOR]

We present an effective proof (with explicit bounds) of the Podelski and Rybalchenko Termination Theorem. The sub-recursive bounds we obtain make use of bar recursion, in the form of the product of selection functions, as this is used to interpret the Weak Ramsey Theorem for pairs. The construction can be seen as calculating a modulus of well-foundedness for a given program given moduli of well-foundedness for the disjunctively well-founded finite set of covering relations. When the input moduli are in system T , this modulus is also definable in system T by a result of Schwichtenberg on bar recursion. [ABSTRACT FROM AUTHOR]

We investigate in intuitionistic first-order logic various principles of preference relations alternative to the standard ones based on the transitivity and completeness of weak preference. In particular, we suggest two ways in which completeness can be formulated while remaining faithful to the spirit of constructive reasoning, and we prove that the cotransitivity of the strict preference relation is a valid intuitionistic alternative to the transitivity of weak preference. Along the way, we also show that the acyclicity axiom is not finitely axiomatizable in first-order logic. [ABSTRACT FROM AUTHOR]

Abstract Recently, a number of formal systems for Nonstandard Analysis restricted to the language of finite types, i.e. nonstandard arithmetic , have been proposed. We single out one particular system by Dinis–Gaspar, which is categorised by the authors as being part of intuitionistic nonstandard arithmetic. Their system is indeed in consistent with the Transfer axiom of Nonstandard Analysis, and the latter axiom is classical in nature as it implies (higher-order) comprehension. Inspired by this observation, the main aim of this paper is to provide answers to the following questions: (Q1) In the spirit of Reverse Mathematics , what is the minimal fragment of Transfer that is inconsistent with the Dinis–Gaspar system? (Q2) What other axioms are inconsistent with the Dinis–Gaspar system? Our answer to the first question suggests that the aforementioned inconsistency actually derives from the axiom of extensionality relative to the standard world, and that other (much stronger) consequences of Transfer are actually harmless. Perhaps surprisingly, our answer to the second question shows that the Dinis–Gaspar system is inconsistent with a number of (non-classical) continuity theorems which one would – in our opinion – categorise as intuitionistic in the sense of Brouwer. Finally, we show that the Dinis–Gaspar system involves a standard part map , suggesting this system also pushes the boundary of what still counts as 'Nonstandard Analysis' or 'internal set theory'. [ABSTRACT FROM AUTHOR]

I see the question what it is that makes an inference valid and thereby gives a proof its epistemic power as the most fundamental problem of general proof theory. It has been surprisingly neglected in logic and philosophy of mathematics with two exceptions: Gentzen's remarks about what justifies the rules of his system of natural deduction and proposals in the intuitionistic tradition about what a proof is. They are reviewed in the paper and I discuss to what extent they succeed in answering what a proof is. Gentzen's ideas are shown to give rise to a new notion of valid argument. At the end of the paper I summarize and briefly discuss an approach to the problem that I have proposed earlier. [ABSTRACT FROM AUTHOR]

An interview with Charles McCarty by Piotr Urbańczyk concerning mathematical explanation.

At the end of the 19th century in the fundamentals of mathematics appeared a crisis. It was caused by the paradoxes found in Cantor’s set theory. One of the ideas a resolving the crisis was intuitionism – one of the constructivist trends in the philosophy of mathematics. Its creator was Brouwer, the main representative was Heyting. In this paper described will be attempt to construct a suitable logic for philosophical intuitionism theses. In second paragraph Heyting system will be present – its axioms and matrices truth-. Later Gödel theorem about the inadequacy of finite dimensional matrices for this system will be explained. At the end this paper an infinite sequence of matrices adequate for Heyting axioms proposed by Jaśkowski will be described.

The field of sociology has long been subject to critique for alleged ideological bias and left-wing groupthink linked to its social justice mission. Critics contend that the construction of “sacred victims” by progressive intellectuals hinders their ability to objectively appraise the circumstances of such vulnerable groups. To address this criticism, we survey 479 sociologists in national universities and colleges in the U.S. regarding three sensitive controversies: urban poverty in the black community; gendered differences in occupational choices; and immigration. We find significant patterns in the data. Commitment to the field’s “moral mission,” preferred research paradigm, gender, and especially political orientation are all significant predictors of sociologists’ views. The results, we suggest, can be understood by conceptualizing the field of sociology as an “emotive community.” In doing so, we draw upon current social psychological research on moral foundations theory developed by Jonathan Haidt and colleagues. [ABSTRACT FROM AUTHOR]

In a recent paper, Wigglesworth claims that syntactic criteria of theoretical equivalence are not appropriate for settling questions of equivalence between logical theories, since such criteria judge classical and intuitionistic logic to be equivalent; he concludes that logicians should use semantic criteria instead. However, this is an artefact of the particular syntactic criterion chosen, which is an implausible criterion of theoretical equivalence (even in the non-logical case). Correspondingly, there is nothing to suggest that a more plausible syntactic criterion should not be used to settle questions of equivalence between different logical theories; such a criterion (which may already be found in the literature) is exhibited and shown to judge classical and intuitionistic logic to be inequivalent. [ABSTRACT FROM AUTHOR]

Husserl claims that his phenomenological-epistemological system amounts to a “universal” form of empiricism. The present paper shows that this universal moment of Husserl’s empiricism is why his empiricism qualifies as a rationalism. What is empiricist about Husserl’s phenomenological-epistemological system is that he takes experiences to be an autonomous source of immediate justification. On top of that, Husserl takes experiences to be the ultimate source of justification. For Husserl, every justified belief ultimately depends epistemically on the subject’s experiences. These are paradigms of empiricist claims and thus Husserl seems to subscribe to empiricism. However, what is universal about Husserl’s “empiricism” is that he does not limit the concept of (justification-conferring) experiences to sensory experiences or sensory experiences plus introspective intuitions but broadens the concept of experience such that also a priori intuitions are included. Husserl insists that logical, mathematical, and phenomenological intuitions such as ~ (p ∧  ~ p), 2 + 2 = 4, and “Experiences necessarily bear the mark of intentionality” provide non-inferential justification analogous to how sensory experiences can non-inferentially justify beliefs such as “There is a table in front of me.” Importantly, Husserl makes clear that such a priori intuitions are not about our concepts but about reality. This is why Husserl’s universal empiricism is a rationalism. Husserl differs from traditional rationalism as he allows that a priori intuitions can be fallible and empirically underminable. This distinguishes Husserl’s rationalism from Descartes’ and makes him a proponent of moderate rationalism as currently championed by Laurence BonJour. [ABSTRACT FROM AUTHOR]

In The Boundary Stones of Thought (2015), Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project. [ABSTRACT FROM AUTHOR]

Copyright of Histórica (02528894) is the property of Pontificia Universidad Catolica del Peru and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Intuitionism and nihilism, according to nihilists, have key features in common: the same semantics and the same phenomenology. Intuitionism is the object of nihilism’s attack. The central charge nihilism lodges against intuitionism is that its nonnatural moral properties are queer. Here I’ll examine what ‘queer’ might mean in relation to the doctrines nihilism uses to support this charge. My investigation reveals that nihilism’s queerness charge lacks substance and resembles a tautology served with a frown. There’s really nothing to it. After I show that, I’ll offer an explanation for why nihilism has gotten intuitionism wrong. It makes a central mistaken methodological assumption and doesn’t target any identifiable intuitionism in the last hundred or so years. [ABSTRACT FROM AUTHOR]

Frege writes in Numbers and Arithmetic about kindergarten-numbers and "an a priori mode of cognition" that they may have "a geometrical source." This resembles recent findings on arithmetical cognition. In my paper, I explore this resemblance between Gottlob Frege's later position concerning the geometrical source of arithmetical knowledge, and some current positions in the literature dedicated to arithmetical cognition, especially that of Stanislas Dehaene. In my analysis, I shall try to mainly see to what extent (Frege's) logicism is compatible with (Dehaene's) intuitionism. [ABSTRACT FROM AUTHOR]

We present a bounded modified realisability and a bounded functional interpretation of intuitionistic nonstandard arithmetic with nonstandard principles. The functional interpretation is the intuitionistic counterpart of Ferreira and Gaspar's functional interpretation and has similarities with Van den Berg, Briseid and Safarik's functional interpretation but replacing finiteness by majorisability. We give a threefold contribution: constructive content and proof-theoretical properties of nonstandard arithmetic; filling a gap in the literature; being in line with nonstandard methods to analyse compactness arguments. [ABSTRACT FROM AUTHOR]

In § 7 of the Critique of Practical Reason Kant presents his first definition of the universal law of morality--called the Categorical Imperative. In the same place, he affirms that being conscious of the law of morality is a Faktum of reason. The ambiguity of this statement has prompted some authors to argue that Kant does not deduce the moral law satisfactorily nor does he clarify how we become conscious of it. Nevertheless, they all forget in their analysis a relevant aspect of Kantian moral philosophy that turns out to be of great importance in contemporary studies of the philosophy of action--the self-constituting character of the rational subject and the role it plays within the foundation of morality. I claim that the Faktum of reason must be understood fundamentally as a self-constituting act. [ABSTRACT FROM AUTHOR]

Motivated by the definition of semi-Nelson algebras, a propositional calculus called semi-intuitionistic logic with strong negation is introduced and proved to be complete with respect to that class of algebras. An axiomatic extension is proved to have as algebraic semantics the class of Nelson algebras. [ABSTRACT FROM AUTHOR]

Peirce and Frege both distinguished between the propositional content of an assertion and the assertion of a propositional content, but with different notational means. We present a modification of Peirce’s graphical method of logic that can be used to reason about assertions in a manner similar to Peirce’s original method. We propose a new system of Assertive Graphs (AGs), which unlike the tradition that follows Frege involves no ad hoc sign of assertion. We show that axioms of intuitionistic logic can be derived from AGs, and argue that AGs analyse and represent assertions and illocutionary content in a way which is motivated both by its logical properties and its historical connection with the ideas that led to the development of the graphical method. [ABSTRACT FROM AUTHOR]

Copyright of Hileya: Scientific Bulletin / Gileya is the property of GILEYA Publishing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)