This article introduces the three-valuedweakly-intuitionistic logicI 1 as a counterpart of theparaconsistent calculusP 1 studied in [11].I 1 is shown to be complete with respect to certainthree-valued matrices. We also show that in the sense that any proper extension ofI 1 collapses to classical logic.The second part shows thatI 1 is algebraizable in the sense of Block and Pigozzi (cf. [2]) in a way very similar to the algebraization ofP 1 given in [8].

In this paper we extend the usual notion of model (asa structure) to the more general notion of CauchySequence of Structures in a similar way as rationalsare extending to real numbers by means of Cauchysequences of rationals. We show that the structurespace Stτ is dense in thecomplete space CStτ of Cauchysequences of structures and that CStτ is compact in the (topo)logicalsense.

In this paper we extend the usual notion of model (asa structure) to the more general notion of CauchySequence of Structures in a similar way as rationalsare extending to real numbers by means of Cauchysequences of rationals. We show that the structurespace St is dense in thecomplete space CSt of Cauchysequences of structures and that CSt is compact in the (topo)logicalsense.

In this paper I want to do the following things. First I want to show that in the part of the Theaetetus where the relationship between knowledge and perception is examined, the concept of knowledge that is in question is very clearly characterized. We are left in no doubt as to what is to count as knowing. Secondly I want to unravel in some detail the case that Socrates puts on Protagoras’ behalf where he draws on what Protagoras actually wrote (...) (151 E-152C); as opposed to what he may have taught secretly to his pupils (152C-160D). Thirdly I wish to argue that if we let the dialogue speak for itself, it is manifest that this case put up on Protagoras’ behalf at 151 E-152C is not overthrown; it is not even shaken. (shrink)

In this paper I want to do the following things. First I want to show that in the part of the Theaetetus where the relationship between knowledge and perception is examined, the concept of knowledge that is in question is very clearly characterized. We are left in no doubt as to what is to count as knowing. Secondly I want to unravel in some detail the case that Socrates puts on Protagoras’ behalf where he draws on what Protagoras actually wrote (...) ; as opposed to what he may have taught secretly to his pupils. Thirdly I wish to argue that if we let the dialogue speak for itself, it is manifest that this case put up on Protagoras’ behalf at 151 E-152C is not overthrown; it is not even shaken.In that part of the dialogue where the question is under examination whether or not knowledge and perception are the same, Socrates uses an idealized concept of knowledge. That is, he restricts the use of the word by setting down what he will consider to be the essential characteristics of knowledge, the sufficient and necessary conditions of its being instantiated. An excellent piece of philosophical procedure. (shrink)

The inverse of the distance between two structures $\mathscr{A} \not\equiv \mathscr{B}$ of finite type τ is naturally measured by the smallest integer q such that a sentence of quantifier rank q - 1 is satisfied by A but not by B. In this way the space $\operatorname{Str}^\tau$ of structures of type τ is equipped with a pseudometric. The induced topology coincides with the elementary topology of $\operatorname{Str}^\tau$ . Using the rudiments of the theory of uniform spaces, in this elementary note (...) we prove the convergence of every Cauchy net of structures, for any type τ. (shrink)

The inverse of the distance between two structures $\mathscr{A} \not\equiv \mathscr{B}$ of finite type $\tau$ is naturally measured by the smallest integer $q$ such that a sentence of quantifier rank $q - 1$ is satisfied by $\mathscr{A}$ but not by $\mathscr{B}$. In this way the space $\operatorname{Str}^\tau$ of structures of type $\tau$ is equipped with a pseudometric. The induced topology coincides with the elementary topology of $\operatorname{Str}^\tau$. Using the rudiments of the theory of uniform spaces, in this elementary note we (...) prove the convergence of every Cauchy net of structures, for any type $\tau$. (shrink)

Because anticipated and retrospective regret play important roles in practical deliberation and motivation, better understanding them can illuminate the contours of human agency. However, the possibility of self-ignorance and the fact that we change over time can make regret—especially anticipatory regret—not only a poor predictor of where the agent will be in the future but also an unreliable indicator of where the agent stands. Granting these, this paper examines the way in which prospective and, particularly, retrospective regret can nevertheless yield (...) important insight into the sorts of creatures we are, both generally and individually. The experience of retrospective regret can show a person she values something in a way she did not know or that she is (or was) a different person than she had thought, insights which can factor into forward-looking, or prospective, deliberation. Such instances of revelatory regret reveal something to the agent about herself as agent. I examine two cases of agential self-ignorance. In the first, the experience of regret reveals what the agent values, not only to others but even to the agent himself. In the second, the agent anticipates experiencing regret for an action but does not experience the regret, suggesting that the agent did not value the rejected alternative in the way she thought. Anticipatory regret is forward-looking and can play an important role in practical deliberation. But insofar as anticipatory regret flows from one’s imperfect judgment and prospection about oneself, retrospective regret can be an important corrective in helping the agent understand her own standpoint. (shrink)

We obtain in this paper a representation of the formulae of extensions ofL by generalized quantifiers through functors between categories of first-order structures and partial isomorphisms. The main tool in the proofs is the back-and-forth technique. As a corollary we obtain the Caicedo's version of Fraïssés theorem characterizing elementary equivalence for such languages. We also discuss informally some geometrical interpretations of our results.

We investigate whether ordinary quantification over objects is an extensional phenomenon, or rather creates non-extensional contexts; each claim having been propounded by prominent philosophers. It turns out that the question only makes sense relative to a background theory of syntax and semantics (here called a grammar) that goes well beyond the inductive definition of formulas and the recursive definition of satisfaction. Two schemas for building quantificational grammars are developed, one that invariably constructs extensional grammars (in which quantification, in particular, thus (...) behaves extensionally) and another that only generates non-extensional grammars (and in which quantification is responsible for the failure of extensionality). We then ask whether there are reasons to favor one of these grammar schemas over the other, and examine an argument according to which the proper formalization of deictic utterances requires adoption of non-extensional grammars. (shrink)

My discussion addresses the differences between analytic and continental philosophy concerning the use of logic and exact reasoning in philosophical practice. These differences are mainly examined in the light of the controversial dominance of Hegel's concept of logic (and theory of concept) in twentieth-century continental philosophy. The inquiry is developed in two parts. In the first (Sections 1-2), I indicate some aspects of the analytic-continental divide, pointing to the role that the topic 'logic and philosophy' plays in it. In the (...) second part (Sections 3-6), I give a short account of the views of logic which are typical of the three main trends of continental philosophy (see Table 1). I also suggest how, with the aid of some typical analytical devices, some continental 'anti-logical' attitudes may be corrected, on their own terms. (shrink)

In his newly updated version of The Anatomy of a Constitutional Law Case, Alan F. Westin provides a documentary portrait of historically important constitutional law case, 'Youngstown Sheet & Tube Co. v. Sawyer, ' from its rise in a bargaining dispute in the steel industry during 1952 to the aftermath of its decision by the United States Supreme Court. Westin has added to his classic book additional materials and personal commentaries collected since the work was first published. The new information (...) covers what went on within the Truman administration, what went on within the Supreme Court when analyzing and resolving issues that come before it. Westin includes selections from transcripts, briefs and other official proceedings, adds notes describing each phase of the constitutional process, and a section of commentary and questions relating this case to others. (shrink)

F. N. Sibley; VIII—Colours, Proceedings of the Aristotelian Society, Volume 68, Issue 1, 1 June 1968, Pages 145–166, https://doi.org/10.1093/aristotelian/68.1.1.

It is not quite as easy to see that there is in fact no formula of this modal language having the same truth conditions (in terms of S5 Kripke semantics) as (1). This was rst conjectured by Allen Hazen2 and later proved by Harold Hodes3. We present a simple direct proof of this result and discuss some consequences for the logical analysis of ordinary modal discourse.

In discussing questions of free will, Soviet philosophers fail to distinguish conditions from causes. This makes them unable to understand the very opponents they like to criticize.

In recent years, there has been a heated debate about how to interpret findings that seem to show that humans rapidly and automatically calculate the visual perspectives of others. In the current study, we investigated the question of whether automatic interference effects found in the dot-perspective task (Samson, Apperly, Braithwaite, Andrews, & Bodley Scott, 2010) are the product of domain-specific perspective-taking processes or of domain-general “submentalizing” processes (Heyes, 2014). Previous attempts to address this question have done so by implementing inanimate (...) controls, such as arrows, as stimuli. The rationale for this is that submentalizing processes that respond to directionality should be engaged by such stimuli, whereas domain-specific perspective-taking mechanisms, if they exist, should not. These previous attempts have been limited, however, by the implied intentionality of the stimuli they have used (e.g. arrows), which may have invited participants to imbue them with perspectival agency. Drawing inspiration from “novel entity” paradigms from infant gaze-following research, we designed a version of the dot-perspective task that allowed us to precisely control whether a central stimulus was viewed as animate or inanimate. Across four experiments, we found no evidence that automatic “perspective-taking” effects in the dot-perspective task are modulated by beliefs about the animacy of the central stimulus. Our results also suggest that these effects may be due to the task-switching elements of the dot-perspective paradigm, rather than automatic directional orienting. Together, these results indicate that neither the perspective-taking nor the standard submentalizing interpretations of the dot-perspective task are fully correct. (shrink)

Are we witnessing progress or regress in the recent increasing popularity and electoral success of populist politicians and parties in consolidated democratic nations? ... Is the innovative use of popular referendum in Great Britain to settle fundamental constitutional questions a progressive or regressive innovation? ... Similarly, is the increasing use of constituent assemblies to change constitutions across the world evidence of progress in democratic constitutionalism, or, a worryingly regressive change back toward unmediated popular majoritarianism? ... This paper reflects on some (...) of the perils and promise of framing such questions with the conceptual couplet of progress and regress. It considers four compelling critiques of the use of ‘progress’ and its cognates in sociopolitical theory, as well as arguing that such concepts are nevertheless ineliminable for our normative theories. The paper concludes by suggesting that we can avoid the most serious problems by employing only conceptions of political progress and regress that are piecemeal, pragmatic, and processual. (shrink)

The dominant neuroscientific theory of spatial memory is, like many theories in neuroscience, a multilevel description of a mechanism. The theory links the activities of molecules, cells, brain regions, and whole organisms into an integrated sketch of an explanation for the ability of organisms to navigate novel environments. Here I develop a taxonomy of interlevel experimental strategies for integrating the levels in such multilevel mechanisms. These experimental strategies include activation strategies, interference strategies, and additive strategies. These strategies are mutually reinforcing, (...) providing a kind of interlevel and intratheoretic robustness that has not previously been recognized. (shrink)