We give alternative characterizations of exact, extendible and projective formulas in intuitionistic propositional calculus IPC in terms of n -universal models. From these characterizations we derive a new syntactic description of all extendible formulas of IPC in two variables. For the formulas in two variables we also give an alternative proof of Ghilardi’s theorem that every extendible formula is projective.

We give alternative characterizations of exact, extendible and projective formulas in intuitionistic propositional calculus IPC in terms of n-universal models. From these characterizations we derive a new syntactic description of all extendible formulas of IPC in two variables. For the formulas in two variables we also give an alternative proof of Ghilardi’s theorem that every extendible formula is projective.

Related Works: Part I: Michael Zakharyaschev. Canonical Formulas for $K4$. Part I: Basic Results. J. Symbolic Logic, Volume 57, Issue 4 , 1377--1402. Project Euclid: euclid.jsl/1183744119 Part III: Michael Zakharyaschev. Canonical Formulas for K4. Part III: The Finite Model Property. J. Symbolic Logic, Volume 62, Issue 3 , 950--975. Project Euclid: euclid.jsl/1183745306.

Related Works: Part I: Michael Zakharyaschev. Canonical Formulas for $K4$. Part I: Basic Results. J. Symbolic Logic, Volume 57, Issue 4 , 1377--1402. Project Euclid: euclid.jsl/1183744119 Part II: Michael Zakharyaschev. Canonical Formulas for K4. Part II: Cofinal Subframe Logics. J. Symbolic Logic, Volume 61, Issue 2 , 421--449. Project Euclid: euclid.jsl/1183745008.

The axioms of projective and affine plane geometry are turned into rules of proof by which formal derivations are constructed. The rules act only on atomic formulas. It is shown that proof search for the derivability of atomic cases from atomic assumptions by these rules terminates . This decision method is based on the central result of the combinatorial analysis of derivations by the geometric rules: The geometric objects that occur in derivations by the rules can be restricted (...) to those known from the assumptions and cases. This “subterm property” is proved by permuting suitably the order of application of the geometric rules. As an example of the decision method, it is shown that there cannot exist a derivation of Euclid’s fifth postulate if the rule that corresponds to the uniqueness of the parallel line construction is taken away from the system of plane affine geometry. (shrink)

We present a complete axiomatisation of the operator of projection onto state in the Duration Calculus relative to validity in DC without extending constructs. Projection onto state was introduced and studied extensively in our earlier works. We first establish the completeness of a system of axioms and proof rules for the operator relative to validity in the extension of DC by neighbourhood formulas, which express the neighbourhood values of boolean DC state expressions. By establishing a relatively complete axiomatisation for (...) the neighbourhood formulas in DC, we then achieve completeness of our system relative to basic DC. (shrink)

In this paper is aproached the Leibnizian project for a General Characteristics. Intended as a instrument to help the limitations and deficiencies of the natural human reason, the General Characteristcs presents itself moreover as a tool for expanding the power of the human thought by adopting and generalizing the methods of the algebraic representation. This goal however entails a difficulty when it is attempted to define with accuracy the extent of the project. At first place appears the problematic relationships that (...) Characteristics maintains with the act of thinking. In our approach is defended the idea that Characterstics expands the power to thinking by improving its ‘semiotical’ nature. Moreover it is raised the issue of the multiplicity of the Characteristics. In fact, Leibniz presents the Caracteristics as a way to resolve a plurality of problems at once, but these many tasks cast serious doubts on the uniqueness of the project, since Leibniz develops actually a plurality of Characteristics. Our response to this issue is that uniqueness can be saved if it is considered the role that the Combinatorial Characteristics or Science of Formulae plays in the project for a General Characteristics. (shrink)

We characterize strict Mittag-Leffler modules in terms of free realizations of positive primitive formulas, and rings over which projectives are trivial in terms of various notions of separability of strict Mittag-Leffler modules. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A dialogue is a strategic activity characterized by an intentional structure of competition and/or cooperation. The truth of the statements is far from being the most important thing in many dialogical situations. It is a commonplace to stress that many linguistic constructions, even if they provoke agreement or disagreement have nothing to do with truth or falsity.In particular the ≪prescriptive≫ or ≪projective≫ formulas express that an action must be done or that it is forbidden. These statements are not (...) upon the world but upon a project of action that cannot in a strict sense be said to be ≪true≫ or ≪false≫.Nevertheless, it appears to be a permanent or at least a recurrent temptation as well as a strategic attitude for a tenant of the ethical naturalism to maintain that some prescriptions are true or false. Fanaticism can be regarded as the assumption that it is true that certain acts of speech are to be morally condemned or forbidden.I consider that every asserted projective statement can be legitimately denied in four different ways: one can reject the normative dimension, the proposed action, the potential actor, the time table. Leaving aside the last two, I use a simple formula to describe the first two moves: A weak form of negation is to deny that there is a prescription to do: ¬JP ≡ I do not judge prescribed to do ‘A’. A stronger opposition is to judge that there exists a norm commanding not to do the action: JP ≡ I judge prescribed not to do ‘A’.As every judgement is itself a speech act exposed to denegation, the action ‘A’ can very well be another judgement and, in particular, another prescriptive statement. For example: JP≫) ≡ I judge as prescribed that you judge as prescribed that ‘A’. We find here one of the expressions of fanaticism.Following the logical type of judgement exposed to condemnation, — do they belong to the category of prescriptions, evaluations, or observations? — I suggest the following hierarchy: 1a. JP≫) 1b. JP≫) 2a. JP≫) 2b. JP≫) 3a. JP≫) 3b. JP≫) In the most ≪fundamentalist≫ of its forms , fanaticism invests a lot of energy to sanction a series of norms concerning observations.Note the apparent paradox: If you consider that this paper defends the prescription not to speak like a fanatic, does it illustrate a weak expression of fanaticism?Hint: My answer would be NO. (shrink)

Visser's rules form a basis for the admissible rules of . Here we show that this result can be generalized to arbitrary intermediate logics: Visser's rules form a basis for the admissible rules of any intermediate logic for which they are admissible. This implies that if Visser's rules are derivable for then has no nonderivable admissible rules. We also provide a necessary and sufficient condition for the admissibility of Visser's rules. We apply these results to some specific intermediate logics and (...) obtain that Visser's rules form a basis for the admissible rules of, for example, De Morgan logic, and that Dummett's logic and the propositional Gödel logics do not have nonderivable admissible rules. (shrink)

The projective plane of Baldwin 695) is model complete in a language with additional constant symbols. The infinite rank bicolored field of Poizat 1339) is not model complete. The finite rank bicolored fields of Baldwin and Holland 371; Notre Dame J. Formal Logic , to appear) are model complete. More generally, the finite rank expansions of a strongly minimal set obtained by adding a ‘random’ unary predicate are almost strongly minimal and model complete provided the strongly minimal set is (...) ‘well-behaved’ and admits ‘exactly rank k formulas’. The last notion is a geometric condition on strongly minimal sets formalized in this paper. (shrink)

We show that the variety of Heyting algebras has finitary unification type. We also show that the subvariety obtained by adding it De Morgan law is the biggest variety of Heyting algebras having unitary unification type. Proofs make essential use of suitable characterizations (both from the semantic and the syntactic side) of finitely presented projective algebras.

This article begins by exploring a lost topic in the philosophy of science:the properties of the relations evidence confirming h confirmsh'' and, more generally, evidence confirming each ofh1, h2, ..., hm confirms at least one of h1, h2,ldots;, hn''.The Bayesian understanding of confirmation as positive evidential relevanceis employed throughout. The resulting formal system is, to say the least, oddlybehaved. Some aspects of this odd behaviour the system has in common withsome of the non-classical logics developed in the twentieth century. Oneaspect (...) – its ``parasitism'''' on classical logic – it does not, and it is this featurethat makes the system an interesting focus for discussion of questions in thephilosophy of logic. We gain some purchase on an answer to a recently prominentquestion, namely, what is a logical system? More exactly, we ask whether satisfaction of formal constraints is sufficient for a relation to be considered a (logical) consequence relation. The question whether confirmation transfer yields a logical system is answered in the negative, despite confirmation transfer having the standard properties of a consequence relation, on the grounds that validity of sequents in the system is not determined by the meanings of the connectives that occur in formulas. Developing the system in a different direction, we find it bears on the project of ``proof-theoretic semantics'''': conferring meaning on connectives by means of introduction (and possibly elimination) rules is not an autonomous activity, rather it presupposes a prior, non-formal,notion of consequence. Some historical ramifications are alsoaddressed briefly. (shrink)

From the point of view of proof-theoretic semantics, we examine the logical background invoked by Neil Tennant's abstractionist realist account of mathematical existence. To prepare the way, we must first look closely at the rule of existential elimination familiar from classical and intuitionist logics and at rules governing identity. We then examine how well free logics meet the harmony and uniqueness constraints familiar from the proof-theoretic semantics project. Tennant assigns a special role to atomic formulas containing singular terms. This, (...) we find, secures harmony and uniqueness but militates against the putative realism. (shrink)

Unifiability of terms (and formulas) and structural completeness in the variety of relation algebras RA and in the products of modal logic S5 is investigated. Nonunifiable terms (formulas) which are satisfiable in varieties (in logics) are exhibited. Consequently, RA and products of S5 as well as representable diagonal-free n-dimensional cylindric algebras, RDfn, are almost structurally complete but not structurally complete. In case of S5n a basis for admissible rules and the form of all passive rules are provided.

Restricted to first-order formulas, the rules of inference in the Curry-Howard type theory are equivalent to those of first-order predicate logic as formalized by Heyting, with one exception: ∃-elimination in the Curry-Howard theory, where ∃x : A.F (x) is understood as disjoint union, are the projections, and these do not preserve firstorderedness. This note shows, however, that the Curry-Howard theory is conservative over Heyting’s system.

The axiom of choice ensures precisely that, in ZFC, every set is projective: that is, a projective object in the category of sets. In constructive ZF (CZF) the existence of enough projective sets has been discussed as an additional axiom taken from the interpretation of CZF in Martin-Löf’s intuitionistic type theory. On the other hand, every non-empty set is injective in classical ZF, which argument fails to work in CZF. The aim of this paper is to shed (...) some light on the problem whether there are (enough) injective sets in CZF. We show that no two element set is injective unless the law of excluded middle is admitted for negated formulas, and that the axiom of power set is required for proving that “there are strongly enough injective sets”. The latter notion is abstracted from the singleton embedding into the power set, which ensures enough injectives both in every topos and in IZF. We further show that it is consistent with CZF to assume that the only injective sets are the singletons. In particular, assuming the consistency of CZF one cannot prove in CZF that there are enough injective sets. As a complement we revisit the duality between injective and projective sets from the point of view of intuitionistic type theory. (shrink)

Suppose T is a weakly minimal theory and p a strong 1-type having locally finite but nontrivial geometry. That is, for any M [boxvR] T and finite Fp, there is a finite Gp such that acl∩p = gεGacl∩pM; however, we cannot always choose G = F. Then there are formulas θ and E so that θεp and for any M[boxvR]T, E defines an equivalence relation with finite classes on θ/E definably inherits the structure of either a projective or (...) affine space over some finite field. We then specify what other structure θ/E may inherit: there is some collection of definable subspaces of finite codimension and some set of algebraic points, which in the affine case may be in the canonically associated vector space, Up to acl, no further structure is possible. If we assume T is weakly minimal and has a strong type p as above, and also that T is unidimensional, we obtain a global description of any model of T in terms of those structures mentioned in the previous paragraph. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Aristotle Rules, OK?José M. Villagrán (bio) and Rogelio Luque (bio)KeywordsAristotle, causes, philosophy, psychiatry, psychopathologyPérez-Alvarez, Sass, and García-Montes (2008) propose a theoretical approach to the nature of mental disorders (MD) that attempts to explain the type of reality they constitute. In line with this approach, they argue that (1) MDs should be considered not from within psychology and psychiatry, but rather from the realm of philosophy, so as to avoid (...) what they call the Charcot effect; (2) the resulting theoretical model is in contrast to naturalist models such as that of internal dysfunction, and involves “strong” constructivist assumptions from which they develop an anthropological perspective based on the clinician–patient situation; 3) this model is applicable, in principle, to all MDs (“at least to some extent”); and (4) it is based on the Aristotelian theory of the four causes.We would argue, however, that (1) it is precisely from within psychology and psychiatry that conceptual models accounting for MDs should be proposed; (2) the naturalist–constructivist dichotomy in these models should be deconstructed, and primacy given not to the ontological approach but to the epistemological one; (3) a theoretical model of this scope should account not only for MDs but also for physical disorders; and (4) only in this way would the Aristotelian theory of causes, understood as types of explanation (and therefore as epistemological approaches) be useful.Approaches from within and from WithoutFor Berrios (2006), the theoretical discourse in relation to the conceptualization of MDs in a particular sociocultural context can be formulated in two ways: on the one hand, in a centripetal fashion, using established philosophical systems (be it phenomenology [Jaspers 1977], logical empiricism [Hempel 1994], or analytic philosophy [Fulford, Thornton, and Graham 2006]). This centripetal approach can be used both by professional philosophers and by psychiatrists/psychologists. When developed by professional philosophers, such proposals, despite their possible brilliance, run the risk of being tangential to the psychiatric issues owing to a lack of first-hand experience of them (Murphy 2006). When developed by psychiatrists and psychologists, the majority of the proposals simply mix fragments of different philosophical systems, in either a kind of syncretism or collage that fails to take into account the contradictions between fragments, or a kind of pluralism that reflects, without entering into analysis, a sort of consensus among the different paradigms (Ghaemi 2003; Kendler 2005).A second way of formulating this theoretical discourse (according to Berrios) would employ a centrifugal approach from the very core of the disciplines, through the reflection of professionals (primarily, although not only, psychiatrists/psychologists with philosophical training) who would conceptualize the problems from within and develop a specific metalanguage for analyzing [End Page 265] them (Lanteri-Laura 1991; Reznek 1991; Sass 1992). Not all problems are of the same type. For those that are extrinsic to psychiatry/psychology (definition of the mental, the mind–body relationship, the distinction between causes and reasons, or interdisciplinary reduction), the methods common to the philosophy of science and of the mind can be used. However, issues intrinsic to the disciplines themselves (the nature of mental symptoms and how they are generated, how to explain their heterogeneity, what a MD is, how to diagnose and classify it, or how to implement a psychopathological project) cannot be dealt with using preestablished formulas, and require new and original proposals that take into account the nature of the disciplines and their object of study (Villagrán 2007).The authors of the target article base their preference for the centripetal approach for responding to one of the intrinsic questions of psychiatry (what MDs are) on the consequences of what they call the Charcot effect, a kind of variant of observer bias applied to psychiatric diagnosis. They offer as an example the classic diagnosis ad iuvantibus in its postmodern version, namely, the efficacy of the pharmaceutical industry in contributing to creating nosological entities for which their drugs are indicated. Consequently, clinicians are not only unable to surmount the substantial epistemological obstacles that hamper attempts to theorize, but also find themselves doomed to assuming an ingenuous essentialism that considers MDs as natural kinds (such as apples, trees, or dogs) determined... (shrink)

The interplay of philosophical ambitions and technical reality have given birth to rich and interesting approaches to explain the oft-claimed special character of mathematical and logical knowledge. Two projects stand out both for their audacity and their innovativeness. These are logicism and proof-theoretic semantics. This dissertation contains three chapters exploring the limits of these two projects. In both cases I find the formal results offer a mixed blessing to the philosophical projects. Chapter 1. Is a logicist bound to the claim (...) that as a matter of analytic truth there is an actual infinity of objects? If Hume’s Principle is analytic then in the standard setting the answer appears to be yes. Hodes’s work pointed to a way out by offering a modal picture in which only a potential infinity was posited. However, this project was abandoned due to apparent failures of cross-world predication. I re-explore this idea and discover that in the setting of the potential infinite one can interpret first-order Peano arithmetic, but not second-order Peano arithmetic. I conclude that in order for the logicist to weaken the metaphysically loaded claim of necessary actual infinities, they must also weaken the mathematics they recover. Chapter 2. There have been several recent results bringing into focus the super-intuitionistic nature of most notions of proof-theoretic validity. But there has been very little work evaluating the consequences of these results. In this chapter, I explore the question of whether these results undermine the claim that proof-theoretic validity shows us which inferences follow from the meaning of the connectives when defined by their introduction rules. It is argued that the super-intuitionistic inferences are valid due to the correspondence between the treatment of the atomic formulas and more complex formulas. And so the goals of proof-theoretic validity are not undermined. Chapter 3. Prawitz (1971) conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister (2019). This chapter resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The chapter further defines a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to allow double negation elimination for atomic formulas and proves the extensional alignment of quasi-proof-theoretic validity and inquisitive logic.Abstract prepared by Will Stafford extracted partially from the dissertation. (shrink)

The author has previously shown that for a certain class of structures $\mathcal {I}$, $\mathcal {I}$-indexed indiscernible sets have the modeling property just in case the age of $\mathcal {I}$ is a Ramsey class. We expand this known class of structures from ordered structures in a finite relational language to ordered, locally finite structures which isolate quantifier-free types by way of quantifier-free formulas. This result is applied to give new proofs that certain classes of trees are Ramsey. To aid (...) this project we develop the logic of EM-types. (shrink)

This thesis is divided into three parts, the first and second ones focused on combinatorics and classification problems on discrete and geometrical objects in the context of descriptive set theory, and the third one on generalized descriptive set theory at singular cardinals of countable cofinality.Descriptive Set Theory (briefly: DST) is the study of definable subsets of Polish spaces, i.e., separable completely metrizable spaces. One of the major branches of DST is Borel reducibility, successfully used in the last 30 years to (...) solve and compare many classification problems. One of our goals is the classification of knots, very familiar and tangible objects in everyday life, which also play an important role in modern mathematics. The study of knots and their properties is known as knot theory. Our plan is to gain insight into knots using discrete objects, such as linear and circular orders. This approach was already exploited in [6]. The first part of this work is therefore devoted to countable linear orders and the study of the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results. We also expand our research to the case of circular orders.Another objective of this first part is to extend the notion of convex embeddability on countable linear orders. We provide a family of quasi-orders of which embeddability is a particular case as well. We study these quasi-orders from a combinatorial point of view and analyse their complexity with respect to Borel reducibility. Furthermore, we extend the analysis of these quasi-orders to the set of uncountable linear orders.The second part of the project deals with classification problems on knots and $3$ -manifolds. The goal here is to apply the results obtained in the first part to the study of proper arcs and knots, establishing lower bounds for the complexity of some natural relations between these geometrical objects. We also obtain some combinatorial results which are particularly interesting when we restrict to the set of wild proper arcs and wild knots, classes which haven’t received much attention so far. These parts are included in the two preprints [4, 5] in collaboration with my supervisor Alberto Marcone, Luca Motto Ros (University of Torino), and Vadim Weinstein (University of Oulu).The second part of this work also includes the classification of non-compact $3$ -manifolds up to homeomorphism (the case of compact $3$ -manifolds has already been solved: indeed, there are only countably many $3$ -manifolds up to homeomorphism; see [7]), and that of Cantor sets of $\mathbb {R}^3$ up to conjugation (answering to Question 5.5 of [3]). Here we resort to algebraic tools. Stone duality gives a neat way to go back-and-forth between totally disconnected Polish spaces and countable Boolean algebras (see [1]). The main ingredient is the Stone space of all ultrafilters on a Boolean algebra. In this work we introduce a weaker concept which we call “blurry filter”. Using blurry filters instead of ultrafilters enables one to extend the class of spaces under consideration beyond totally disconnected. As an application of this method, we show that both homeomorphism on non-compact $3$ -manifolds and conjugation of Cantor sets in $\mathbb {R}^3$ are completely classifiable by countable structures. These results are part of an upcoming paper in collaboration with Vadim Weinstein.The last part of this thesis concerns the natural generalization of descriptive set theory that occurs when countable is replaced by uncountable, called Generalized Descriptive Set Theory (briefly: GDST). In particular, we focus on the case of GDST for a singular cardinal $\kappa $ of countable cofinality. The goal here is to study the generalizations of the Perfect Set Property and the Baire Property to subsets of spaces of higher cardinalities, like the power set $\mathcal {P}(\kappa )$. We consider the question under which large cardinal hypotheses classes of definable subsets of these spaces possess such regularity properties, focusing on rank-into-rank axioms, like I2, and classes of sets definable by $\Sigma _1$ -formulas with parameters from various collections of sets. The obtained results are included in [2], a joint work with my co-supervisor Vincenzo Dimonte and Philipp Lücke (University of Hamburg).Abstract prepared by Martina IannellaE-mail: [email protected]: https://air.uniud.it/handle/11390/1262824. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Sinai and the Areopagus:Philip Melanchthon, Natural Law, and the Beginnings of Athenian Legal History in the Shadow of the Schmalkaldic WarAlexander D. BatsonIn late August 1546, Philip Melanchthon had some seriously strange dreams. One night, he saw a man in the Elbe struggling to keep his head above the river's powerful current. As Melanchthon approached to help, he recognized the drowning man's visage: Charles V. Despite Melanchthon's attempts to (...) save him, the river dragged the emperor under and carried him away. Another night, he dreamed that while translating Demosthenes with his friend Joachim Camerarius in the Wittenberg castle (a Melanchthon dream if there ever was one!) he looked out a window to see that the Elbe had turned to blood.1 [End Page 713]These ominous visions reflected the precarious world Melanchthon faced in late summer 1546. Martin Luther, the hero of the German Reformation, had died in February, leaving a gaping hole in the evangelical movement. Further, German Protestantism was facing the largest political crisis in its short history. The Schmalkaldic War had begun in July, only a few weeks prior, and the Reformation faced intense military pressure from Charles V. As the emperor slowly advanced, an anxious Melanchthon lived in constant tension between wild hope that Charles would be defeated and grim fear of massive bloodshed.As the war began, Melanchthon was greatly disturbed by the violence and the potential for disastrous defeat of the Protestant cause. In an August 26 letter, he wrote this to a friend: "Often now, when I look over the Elbe River gliding by me, I sigh and think that, even if I could pour forth a river of tears as great as the Elbe's flow, I would never be able to exhaust the sadness which surrounds my soul because of this civil war. If only Charles had not started it!"2 Should the Schmalkaldic League be defeated and political support for the Reformation be crushed, the true church would be in dangerous waters, just like the emperor in Melanchthon's dream.In the midst of this impending catastrophe, on September 1, 1546, Melanchthon published an unusual work: the Collatio actionum forensium Atticarum et Romanarum praecipuarum (A comparison of the principal Attic and Roman legal actions). In this study, Melanchthon organized and compared the legal actions of Athens and Rome, following the order of the Ten Commandments. In 1546, Greek law was a virtually unknown field. Contemporary legal humanists like Andrea Alciato, Ulrich Zasius, and François Baudouin had devoted their attention almost exclusively to Roman or feudal European law.3 Nearly a century before the publication of sprawling [End Page 714] tomes by the Greek legal scholars Samuel Petit, Claudius Salmasius, and Johannes Meursius, Melanchthon treated the law of ancient Athens as a worthy subject.4 Even more puzzling, Melanchthon devoted himself to this arcane work during a moment of dire political crisis. The unusual subject matter of the Collatio and the urgent circumstances surrounding its publication raise a pair of intriguing questions: Why did Melanchthon think Attic legal actions were important? And why did he think they were worth studying while a military and political disaster loomed on the horizon?Melanchthon valued the ancient pagan laws because they showed how God had revealed legal and moral principles to the gentiles. His study of Attic and Roman law demonstrated how, through natural reason, the classical pagans had attained knowledge of the natural law and implemented it in their own societies.5 As a result, the ancient laws became indispensable to Christians studying law and moral philosophy.6 This work on ancient Greek law was an essential part of Melanchthon's pedagogical project of integrating Christianity and the classical world. As he wrote in the introduction, he had decided to write on Attic legal actions "so that students may know that they are not only formulas for litigation, but also a philosophy and a doctrine of virtue."7 By reconstructing the laws of ancient Athens and comparing them with those of Rome, Melanchthon demonstrated that classical moral and legal thought was in complete agreement with the Decalogue and essential for Christian moral development. [End Page 715... (shrink)

We establish the bi-modal forgetful projection of the Logic of Proofs and Formal Provability GLA. That is to say, we present a normal bi-modal provability logic with modalities □ and whose theorems are precisely those formulas for which the implicit provability assertions represented by the modality can be realized by explicit proof terms.

This paper presents the case of the post-crisis discursive defence of shadow banking in the Netherlands to argue, first, that there is a need to dust off older elite theories and adapt them to post-democratic conditions where there are no widely shared ‘political formulas’ to secure mass support for elite projects. Second, that temporality should be taken more seriously; it is when stories fail that elite storytelling can be observed in practice. As new ‘political formulas’ are minted and (...) become established, elites can again hope to withdraw from the political scene and leave policy-making to the self-evidence of output legitimacy and/or the perpetuum mobile of There-Is-No-Alternative. This suggests that elite theory should replace an epochal reading of post-democracy with a more conjunctural one. (shrink)

Representing moral choice as a function of rational choice is carried out by formalizing moral evaluation into a functional mechanism called "Moral Choice Function" whose domain is information on a state of affairs and range is a moral judgment, and upon which formal and substantive requirements are imposed. The notions such as impartiality, universalizability, proportionality, and informational invariance are employed for the issue of how to solve conflict of values faced by an individual as well as collective moral agent. By (...) utilizing the structural affinity with post-Arrovian social choice theory, it is shown that inter-attribute commensurability is indispensable for any serious moral agent who wants to solve conflict of values through pluralistic maximizing. It is also shown that once the morally relevant attributes are identified, formal requirements are powerful enough to qualify the function to behave in a certain way such that the formulas for pluralistic maximizing vary with the modes of inter-attribute commensurability. It is also shown how it is still possible to manage conflict of values rationally without value commensurability by interpreting John Rawls's theory of justice as neo-Kantian in dealing with conflicting desiderata from Kantian deontology and utilitarian consequentialism. The metaethical tenets for the project are also argued for such that it is neutral about the ontological status of morality; but it is anti-Humean with its supervenience thesis, anti-Moorean with its reducibility thesis, and anti-naturalist with its syntheticity thesis. It is also argued that behind the project there lies a fundamental metaphysical conception of an entity as a bundle of properties conjoined with epistemic foundationalism, which is evidenced not only in moral evaluation but also in other kinds of cognitive activity. (shrink)

We present a semantic game for Gödel logic and its extensions, where the players’ interaction stepwise reduces arbitrary claims about the relative order of truth degrees of complex formulas to atomic ones. The paper builds on a previously developed game for Gödel logic with projection operator in Fermüller et al., Information processing and management of uncertainty in knowledge-based systems, Springer, Cham, 2020, pp. 257–270). This game is extended to cover Gödel logic with involutive negations and constants, and then lifted (...) to a provability game using the concept of disjunctive strategies. Winning strategies in the provability game, with and without constants and involutive negations, turn out to correspond to analytic proofs in a version of \ :1941–1958, 2010) and in a sequent-of-relations calculus, Automated reasoning with analytic tableaux and related methods, Springer, Berlin, 1999, pp. 36–51) respectively. (shrink)

When we ask ourselves about the meaning of life, two analyses are possible in principle: 1. that we are asking something about the purpose or the reason of being of life or of a life, or 2. that we are asking something the value of life or of a life. At the present article, I do not approach 1 neither the life as a whole, but I take the individual lives in the context of 2. I briefly explain what would (...) be to someone to have an objectivist conception of the meaning of life and what would be to someone to have a subjectivist one; and, then, I try to show how we can think in formulas that can capture the intuitions of those conceptions, without acquiring commitment with none of them. My way is to show that both objectivist and subjectivist conceptions think the meaning of life as related to projects or realizations that fulfill principles of value (the value can be objective or subjective according to the adopted conception), and ten I try to indicate that the projects or realizations from a person’s life come together through a simple sum to make the meaning of life of such a person’s life. The way I suggested for us to find the value of one of those realizations does not seem to present none theoretical problem. But the simple sum of realizations (and/or projects) to represent the value of the meaning of a person’s life simply did not work. That’s because it seems to lack some kind of index that is able to formalize the relations between realizations. Thus, although we couldn’t properly formalize the relation between the realizations that achieve the meaning of someone’s life at a certain moment, we get a good intuitive formalization of the value of a realization and we hope to have started an interesting investigation for future logicians, metaphysicians, mathematicians and theorists of value. (shrink)

The structural view of rational acceptance is a commitment to developing a logical calculus to express rationally accepted propositions sufficient to represent valid argument forms constructed from rationally accepted formulas. This essay argues for this project by observing that a satisfactory solution to the lottery paradox and the paradox of the preface calls for a theory that both (i) offers the facilities to represent accepting less than certain propositions within an interpreted artificial language and (ii) provides a logical calculus (...) of rationally accepted formulas that preserves rational acceptance under consequence. The essay explores the merit and scope of the structural view by observing that some limitations to a recent framework advanced James Hawthorne and Luc Bovens are traced to their framework satisfying the first of these two conditions but not the second. (shrink)

In this paper we look at two classic methods of deriving consequences from inconsistent premises: Rescher-Manor and Schotch-Jennings. The overall goal of the project is to confine the method of drawing consequences from inconsistent sets to those that do not require reference to any information outside of very general facts about the set of premises. Methods in belief revision often require imposing assumptions on premises, e.g., which are the important premises, how the premises relate in non-logical ways. Such assumptions enable (...) one to select a reasonable collection of formulas from all the formulas of the language. Basic versions of the classic methods only use logical relations between the premises. We compare and criticize each of the classic views with an eye to combining the views to get the most out of inconsistent premises. We do this in a way that will respect the theoretical grounding of each view while meeting our other restrictions. (shrink)

In the late 1960s and early 1970s, Dana Scott introduced a kind of generalization (or perhaps simplification would be a better description) of the notion of inference, familiar from Gentzen, in which one may consider multiple conclusions rather than single formulas. Scott used this idea to good effect in a number of projects including the axiomatization of many-valued logics (of various kinds) and a reconsideration of the motivation of C.I. Lewis. Since he left the subject it has been vigorously (...) prosecuted by a number of authors under the heading of abstract entailment relations where it has found an important role in both algebra and theoretical computer science. In this essay we go back to the beginnings, as presented by Scott, in order to make some comments about Scott’s cut rule, and show how much of Scott’s main result may be applied to the case of single-conclusion logic. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.3 (2003) 416-417 [Access article in PDF] Jean-Baptiste Rauzy. La Doctrine leibnizienne de la vérité. Aspects logiques et ontologiques. Paris: Vrin, 2001. Pp. vii + 353. Paper, FF 170,55.This important book provides a reappraisal of Leibniz's philosophy of logic and epistemology based on a close scrutiny of the recently edited manuscripts in the Akademie-Ausgabe, and a reconstitution of Leibniz's sequential investigations. The author (...) displays an exceptional knowledge of the Leibnizian corpus, the ancient and medieval sources for the various doctrines he analyzes, and the contemporary issues underpinning Leibniz's investigations. He aims at rectifying misconceptions that stemmed originally in Couturat's La Logique de Leibniz (1901) and have since affected several studies. Three methodological statements set the ground for Rauzy's analysis: (1) Leibniz's notion of truth concerns in unified fashion all the elements of discourse: terms, concepts, and propositions. (2) Leibniz did not restrict his doctrine of truth to consistency relations, but yielded a complex, well-articulated conception of truth as correspondence, as evidenced in New Essays on Human Understanding, IV, v, sect. 11; yet, at the same time, his doctrine focused on conceptual relations which specify an order of reasons deserving to be analyzed for their own sake: "Dans la doctrine leibnizienne de la vérité, l'adaequatio rei constitue encore le cadre général en dehors duquel le prédicat de vérité n'a pas de sens. Mais les concepts et les liaisons conceptuelles donnent désormais la raison pour laquelle telle phrase particulière est vraie..." (47). And (3) one should resist attributing to Leibniz a purely syntactic conception of truth since the semantic dimension of his logical analyses deserves to be reconstituted and due consideration should be given to the evolution of his thoughts on central philosophical issues, which occasioned significant variations in the elements and formulas of his calculus rationis.It is merely possible to render the rich contents of the book by mentioning some of its more striking features. In Chapter 1, the inesse principle (Praedicatum inestsubjecto) is shown to serve grammatical, logical, and conceptual functions. The doctrine of expression is finely analyzed: expression is shown to provide the major translation tool between characters and thoughts and to condition the combinatorial treatment of rational discourse. In Chapter 2, the distinction between concept and object is shown to involve some relativity, even if the understanding of complete notions is supposed to entail real knowledge of the corresponding realities. Leibniz is thus justified to represent the manifold of ontological relations, including the requisites of actual existence, in a tentatively unified logical way: "Que [End Page 416] l'existence soit une propriété relationnelle complexe, conçue tantôt par la relation de compatibilité, tantôt par une relation à l'esprit en général—et éventuellement [...] par un mixte des deux—n'interdit nullement de maintenir que la vérité de toutes les propositions dépend de relations conceptuelles" (124-5). In Chapter 3, the project of a calculus based on concepts is shown to entail a special relation, hardly dealt with in the literature, between intension and extension (cf. for instance New Essays, IV, xvii, sect. 8). Rauzy reassesses in particular Leibniz's critical revision of nominalism and of inductive procedures as these require universal propositions to ground rational presumptions. The extensional notion of class is considered an abstraction: a class presupposes therefore the extension of a concept in order to become an object of thought. The principle of conceptual inherence requires to be interpreted as stating the equipollence between the requisites of subject and predicate; if such an equipollence may be reached a priori in exceptional cases, most of the time it will require various kinds of additions and derivations to yield sufficient congruence between the related terms. Chapter 4 is devoted to substitutions, more precisely to the theory of definition and the context, at once logical and discursive, from which a potential Leibnizian theory of communication might be derived. Rauzy notes that substitutive equivalences... (shrink)

Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [4] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. Jónsson in [3]. Other authors have extended this result to the cases (...) of k-deductive systems and of consequence relations on associative, commutative, multiple conclusion sequents. Our main result subsumes all existing results in the literature and reveals their common character. The proofs are of order-theoretic and categorical nature. (shrink)

In section 1 we present moral constructivism as a metaphysical project which grounds moral norms in the attitude of valuing by rational agents. In section 2 we establish that Kantian Constructivism – opposed to Humean Constructivism – seeks objective and universal moral norms through a process of rational construction and ratification of norms that does not draw on any kind of subjective attitude of valuing. In section 3 we explore whether Kant is a moral constructivist or moral realist, arguing that (...) he might be read as a proto-moral constructivist whose formulas impose standards of correctness upon our moral judgments, from which we formulate moral norms as necessary facts of reason. In section 4 we argue that: 1) vulnerabilities have moral relevance which adds merit to the project of finding objective moral norms, and 2) the inclusion of vulnerabilities as empirical contingencies is compatible with Kantian Constructivism. We do so by considering vulnerabilities a constitutive aspect of finite rational agents which must, therefore, be implied and considered in the process of moral construction. (shrink)

This introduction just aims to be a fast foreword to the special topic now turned into an e-book. The Editorial "Decision-Making Experiments under a Philosophical Analysis: Human Choice as a Challenge for Neuroscience" alongside with my opinion article "Neurophilosophical considerations on decision making: Pushing-up the frontiers without disregarding their foundations" play the real role of considering in more details the articles and the whole purpose of this e-book. What I must highlight in this foreword is that our intention with such (...) a project was to deepen into the very foundations of our current paradigms in decision neuroscience and to philosophically moot its foundations and repercussions. Normal Science (a term coined by Philosopher Thomas Kuhn) works under a research consensus among a scientific community: A shared paradigm, consolidated methods, widespread convictions. Pragmatically, winning formulas must be kept, although, not at any cost. What differentiates a gifted and revolutionary scientist from a more bureaucratic colleague is the capacity and willingness of constantly reevaluating, depurating and refining his/her own paradigm. That is best strategy to avoid that a paradigm itself would gradually come under challenge. In my view, some achievements, in this sense, were brought about in our project. The e-book will be inspiring and informative for both neuroscientists that are concerned with the very foundations of their works and for philosophers that are not blind to empirical evidence. Kant once said: “Thoughts without content are empty, intuitions without concepts are blind”. Paraphrasing Kant we could say: Philosophy without science is empty, science without philosophy is blind. (shrink)

Due to the currently insufficient consideration of task fitness and task coordination for task allocation in collaborative customized product development, this research was conducted based on the analysis of collaborative customized product development process and task allocation strategy. The definitions and calculation formulas of task fitness and task coordination efficiency were derived, and a multiobjective optimization model of product customization task allocation was constructed. A solution based on adaptive genetic algorithm was proposed, and the feasibility and effectiveness of the (...) task allocation algorithm were tested and verified using a 5-MW wind turbine product development project as example. (shrink)

I. INTRODUCTIONThe Parshall Flume, which was invented in 1920 by R. Parshall, is mostly used in wastewater and crop supply. Utilizing equations, Parshall established dimensions that fit the design, one of the advantages is the conversion of position energy to velocity energy since in other measurement structures there are minimum energy losses in this one it does not allow sedimentation. The structuring of the project is adhered to by different models that define its behavior and limit its use. This is (...) the case of an approach length of the channel entrance, which is nothing more than a primary distance for the action of the flow within the channel. Throughout history, some studies were conducted in an attempt to establish an approximate and realistic value of the length at the time of measurements, but the theories put forward were lost. Some people link this length with the narrowing of the gorge, and others suggest flow conditions before entering the flume. For the development of the project established with its respective objectives, the respective structuring was carried out: For the measurement, the points already established in the field will be taken with the help of a total station, GPS, to verify the respective measurements of the Parshall flume. For the calculations and the design, the points will be introduced in the civil 3D to be able to verify if the points taken are the correct ones and what distances they have between them, through this, we can apply different methods to be able to verify the design that has this Parshall flume. For the evaluation and layout of the gutter, if it is the case, we will carry out a layout in plan with the data already calculated in the office and we will evaluate the situation in which it is so that we can apply a possible solution so that a defect does not occur. In this report, we focus on the design and redesign of a hydraulic irrigation channel where we find a Parshall section, which has the function of measuring the flow found in that section. The measurements found in the field can be verified in the office using formulas and software to verify if the data are correct, if so we can say that it is well designed, otherwise we will look for a possible solution by doing a field study. (shrink)

Architecture and Deconstruction Case of Peter Eisenman and Bernard Tschumi -/- Introduction Towards deconstruction in architecture Intensive relations between philosophical deconstruction and architecture, which were present in the late 1980s and early 1990s, belong to the past and therefore may be described from a greater than before distance. Within these relations three basic variations can be distinguished: the first one, in which philosophy of deconstruction deals with architectural terms but does not interfere with real architecture, the second one, in which (...) a collaboration between Jacques Derrida and a group of architects interested in his concepts is commenced, and the third one, in which completed or only designed objects or new concepts of deconstruction created by architects gain their supremacy over philosophy. The following book analyses these three possible ways, first of all with the reference to Peter Eisenman and Bernard Tschumi. -/- Peter Eisenman -/- Misreading… and Other Errors -/- The issue of relations between Peter Eisenman’s work and philosophy of deconstruction may be referred to his activity more than ten years preceding his direct collaboration with Jacques Derrida (in 1985) and organisation of the exhibition Deconstructivist Architecture at Museum of Modern Art in New York (in 1988). As soon as at the stage of designing the first houses (House I-III, 1967-1970), which almost entirely inscribed in formalistic aesthetics of Modernism, the architect analysed the problem of architecture dependence on its assumptions. All his later designs may be treated as consequence of this initial interest in relations between practice and theory, and at the same time as an introduction to manipulations later on led at the level of metaphysics of architecture. Beginning with the issue of presence, considered in comments to House VI (1972), the number of ideas having their analogies in philosophy of deconstruction increased. The text entitled The End of the Classical: The End of the Beginning, The End of the End (1984), in which Eisenman criticised questions of representation in architecture, its delusive strive for truth and comparably unattainable attempts at ultimate definition of elementary rules, should be acclaimed the breaking point. This attitude was extended by numerous strategies disturbing architecture rules defined at metaphysical level in an essay Moving Arrows, Eros, and Other Errors: an Architecture of Absence (1986). The issue of Eisenman’s passage from formalism to deconstruction has already been much discussed in the literature (Rosalind Krauss, Thomas Patin among others), still it should be mentioned that the threads similar to Derrida’s concept included in Eisenman’s writing reveal untranslatability of architecture and philosophy. -/- Choral Works or Separate tricks -/- In 1985-1986 a series of seven disputes between Jacques Derrida and Peter Eisenman took place. The pretext for them were designs concerning Parc de la Villette in Paris. The situation of many months of collaboration between a notable philosopher of the second half of the 20th c. and an architect that already had a huge theoretical oeuvre, ended up with a publication of a large volume entitled Chora L Works and it became at the same time a vast study area for historians of contemporary architecture and philosophers. Derrida’s contribution to concept works were his considerations over the idea of chôra, the properties related to this concept were about to be reflected in shapes of the park. Therefore, Chora L Works became an example of the abilities of contemporary art, both in its capability of translation from philosophical ideas to artistic forms and its resistance to tradition of representing in architecture some phenomena and values originating outside this discipline. In the final period of their collaboration both interlocutors started to polemicise with each other more decidedly, what became a separate part of their thought exchange. The exchange of letters between Derrida and Eisenman at the turn of 1989 ended up the period of their direct contacts, nevertheless, at this time precisely a large group of experts in issues of deconstruction joined the discussion and extended the revealed in the former dispute problems into more than ten years of further considerations and publications. Except for a long text by Jeffrey Kipnis, who had participated in the meetings of the philosopher and the architect, there appeared also comments of researchers of artistic theories (K. Michael Hays, Thomas Patin), philosophers (Andrew Benjamin), and even experts in Greek literature (Maria Theodorou or Ann Bergren). Following these debates a contemporary reflection on architecture has saturated with indeed numerous concepts originating in philosophy of deconstruction. -/- Architecture which imitates mute philosophy -/- The series of Jacques Derrida and Peter Eisenman meetings, which took place in the period of 1985-1987, induced many authors to make comments. Some of them (Jeffrey Kipnis, Ann Bergren, Maria Theodorou) developed the subject of chôra which was introduced to the discussion by Derrida. The problem that was about to be solved was the question of tying up the concept of chôra with architecture, including Eisenman’s architecture and the series of meetings within frames of Chora L Works project. Kipnis on this occasion paid attention to chôra and its character of anachronia which infects any being created within chôra. In other words any event has its counterpart (analogon) in another, earlier event. He demonstrated the similarity of structure of many events and statements from the times of Derrida and Eisenman’s meetings to the almost identical behaviour of figures in Plato’s dialogue Timaeus. The loss of beginning present in this phenomenon was appropriate to both features of chôra and the effects of typical analyses of philosophy of deconstruction. Bergren’s analyses focused on accentuating gender of chôra, which, according to this author, had been neglected hitherto in discussions. She collated chôra descriptions with characteristics of women in myths, early Greek epic and philosophy and she arrived at a conclusion that chôra has features of a single woman and a married one at the same time. And yet Theodorou’s studies showed that in the Homeric epics chôra is not treated as an idea but is related with single things and events. The other part of the comments (represented by Andrew Benjamin and K. Michael Hays’ utterances) concerns Eisenman’s attitude to tradition which was treated as a variety of iteration understood philosophically. Benjamin commenced his considerations at the point of closeness between a definition of tradition and a concept of chôra understood as perpetuation (placement). A problematic issue was for him Eisenman’s complex relation to tradition based on its contest and affirmation at the same time. Overcoming the simple subordination to tradition – according to Benjamin – was based on awareness of the role of repetition in culture not known before. Hays made an attempt to explain the pleasure and torment of repetition with the support of Sigmund Freud and Roland Barthes’ concepts. According to Hays repetitions are attempts of a single being to a certain primal state perceived as free of any tension. In a similar way Rosalind Krauss explained a motif of a grate present in Modernistic art and also exceptionally frequent in Eisenman’s work. -/- Annex Architecture is still writing Balzac novels. Peter Eisenman and literature -/- Architecture’s approach to writing, script or literature, present within Peter Eisenman’s work, is an exceptional phenomenon, furthermore a complex one. The article considers four possible relations. The first one relates to Eisenman’s characteristics as a person extremely gifted with the ability to wordplay, which very ‘play’ reveals skills to create architectural images. In the second approach the attention has been paid to Eisenman’s interests – in the first period of his oeuvre – in linguistic works by Noam Chomsky and his transformational-generative grammar. The third kind of relations applied to overcoming the need for autonomy of architecture (and of modernist aesthetics at the same time) and renew interests in questions of meaning in architecture. The fourth sort of relations occurred when Eisenman started to create reflections of historic or literary narrations in architecture – ‘stone stories’ and architectural fictions of their kind. -/- Bernard Tschumi -/- From perversion to deconstruction In Bernard Tschumi’s writings from the 1970s and 1980s we can find a transposition of important threads of post-structuralist ideas deriving from Georges Bataille, Roland Barthes and Jacques Derrida’s works. The analysis of the architect’s writings also shows roots in Phillippe Sollers, Michel Foucault and Denis Hollier’s works. The analysis of borrowed elements from the beginnings of Tschumi’s theoretical activity may be helpful in explaining the contents of his later writings motre inspired by philosophy of deconstruction. The set of his earliest views was inspired by Marxism, Neo Marxism and French Structuralism, mainly by the writings of Henri Levebre and Guy Debord. From the thought of Levebre Tschumi took interest for city as not only a question of urbanistics but also a political issue. From Debord’s concepts he borrowed a conviction about the role of situational violation for changes in the society structure. Some of these beliefs were preserved in his own concepts of architecture as an event. From this period derived also his will to change conservative elements of social structure not by means of political revolution but of theoretical and creative activity. Tschumi acknowledged that the effective way of the proceedings towards achieving his aims would be accepting the role of both a critical intellectualist and architecture expert who would not hide away his left-wing orientation. The speculations defined by the architect as ‘revolting analyses’ were about to characterise contradictions which tear the society apart, penetrate architecture and constitute the basis of culture. Spreading away of the conscience of false assumptions hidden away in various disciplines could have weakened cohesion of a conservative society and influence the will to change among the elites. This way the beginnings of political revolution were rooted in philosophy of architecture. In 1977 Tschumi published his text entitled The Pleasure of Architecture inspired by Roland Barthes’s The Pleasure of the Text, it also included some concepts derived from Georges Bataille and Jacques Derrida. First of all the author used Barthes’s concept which made an assumption that literary activity is pervaded by the spirit of resistance towards social rules, and Tschudi transferred this remark onto architecture. From the ideas of Bataille, acquainted via Holier’s work, he derived his belief that two concepts of space, a conceptual one (defined as Pyramid) and a sensual one (defined as Labirynth), not losing their distinct features, they join in the concept of experienced space which exceeds contradictions. The exceeding itself was defined as the basic rule of architecture and it was referred to situations in which architecture not only negates social needs, but also disavows its own tradition. Crossing the borders applies not only to political issues or permanent rules of the very discipline but also interfering with other fields (especially literature and film). The fact that architecture is associated with organising events turned Tschumi’s attention to questions of violence that result from upsetting architectural order of a given building by its users and the one hand, and on the other from forcing the users to specific acts imposed by this very order. The analysis of the concepts used by Tschumi in his early writings indicates that they are close to definitions that would occur in his reflection in the following years influenced by philosophy of deconstruction. -/- Approaching deconstruction Tschumi in his theories developed in the 1980s presumed that the current social world had undergone a deep process of decay, and the reaction against which ought to be based on ordering-up actions, and also preserving the main outline of disintegration of the whole and its elements in the state of conflict. The statements concerning the nature of the contemporary to Tschumi social relations were applied by him to the world of architecture, this led him to coming up with designing strategies that took into consideration the destabilised character of conditions in which works of architecture were created. New ways of conduct invented by Tschumi drew their inspiration from literature and research on literature, psychoanalysis, structural linguistics, structuralism and post structuralism, and eventually also deconstruction philosophy. The proposed methods were opposed by their author both to functionalism continuity trends and postmodern architecture. Tschumi’s proposals contradicted any forms of conservatism or traditionalism in political sphere as well as in reference to tendencies in architecture. They were not simple contradictions of social or architectural rules, they intrude them from the inside, weaken or escalate the already existing incongruities, they move the boundaries between the areas. Revolutionary illusions about the possibility of radical changes were replaced with strategies which completed, tainted or test former rules in the series of formal games of permutation and combination. Quite different from avant-garde formalism Tschumi’s games were not about maintaining the autonomy of a given area, but on the contrary – polluting it with other areas’ influences. Tschumi enjoyed demonstrating illusions of architecture concerning simple relations between form and function, or between form and meaning. Making use of Freud, Lacan and Foucault’s research he introduced a category of “madness” into architecture allowing an observation that the recognised norms are nothing but merely ones of many possible principles of behaviour, and their recognised status resulted from unjustified hindering innovativeness which is crucial for architecture. To reborn architecture’s capability of changing Tschumi also made use of Barthes’s discoveries concerning rules of narration and works by writers who applied in their writing knowledge on linguistics. Making a work’s author unclear by various mechanical transformations of its elements was however apparent only, and formal rigours imposed on the process of designing liberated possibilities difficult to obtain in more traditional creative action. Another mode of acting introduced by Tschumi was combining his work of elements deriving from outside architecture; joining space records with notation of motion and events accompanying architectural objects among others. These architectural and extra-architectural elements were not unified, on the contrary their heterogenous and conflictual character was stressed. This is how shock, anxiety and instability, typical for live in great metropolises, infiltrated architecture. Taking some ideas of deconstruction philosophy as a pattern Tschumi also took into critical consideration in his essays traditional in architecture oppositions between form and figuration, or theory and practice. By combining various inspirations he eventually worked out an idea of architectural event, which he understood as a series of actions contesting its own field, redefining its sources, principles and elements. An event, understood in this way, was not so much producing works as rather creating conditions of their production and at the same time designing the society different from a hierarchic one. -/- Park of deconstruction Among numerous philosophical strategies of deconstruction most frequently used was questioning the practice of strong opposition of two reasons. In many cases Bernard Tschumi’s writings just consider functioning of the conflict juxtaposition of the ideas of structure and ornament or theory and practice in history of architecture. Violation of traditional relations between terms of this kind, both old and modern, raised Jacques Derrida’s objections, when he was induced for the first time to co-operate with architects’ milieu. During this long lasting thought exchange the philosopher eventually acknowledged Bernard Tschumi’s arguments for reasoning the encroachment of architecture’s fundamental rules. Deconstruction applied in architecture was not a simple transposition or analogy of practices that had been applied by philosophy of deconstruction. We may even say that considering architectural terms became an important formula of deconstruction. Architecture understood in philosophical way became something beyond the practice and theory of its own discipline, a sort of metaphysics of both philosophy and architecture. The deliberate encroachment of simplicity of dividing architecture into theory and practice, for the first time became a clear aim for Tschumi in his drawings and texts entitled The Manhattan Transcripts. The contents of this series of works was a record of characteristic features of this New York district in such a way that not only objects were the subject of the record but also relations between objects, people and events. The record was about to take into consideration a conflict character of elements of this representation and at the same time to avoid applying to them the rule of mimetism. The record became a form of reflection over the very record by an increased control over the ways of representation. Architecture which was considered in the The Manhattan Transcripts was not directed to fulfill the needs of inhabitation or production, it was rather related with hitherto usually marginalised liminal situations: building ostentatiously big monuments, religious cult, war etc. Architecture operating in these relations focused also the attention on the included in it continuous tendency to overpass its own restrictions, the role of violence as its not recognised factor, or the meaning of excess and shock in its operation. Architecture moving from reason towards madness became even more visible in the design of Parisian Parc de la Villette, whose pavilions were defined as folies (in French it means both small park buildings and follies). The park was supposed to be on the one hand a reflection of traditional society disintegration while on the other it questioned basic rules of producing a work of architecture. The traditional rules of designing, based on ordering up, were replaced with the strategies of dysfunction and dissociation. In Tschumi’s opinion methods of this kind may be equivalent of what Derrida named différance. Instead of aiming at mergence, any diversity, plays or variations were strengthen. Tschumi’s texts, in which he explained his attitude, were completed by Derrida’s extent statement entitled Point de folie – Maintenant l’architecture. Derrida’s article is the most significant of all his statements on architecture as a form of thinking and activity. According to the philosopher, architecture should divide space (in French defined as espacement), what enables both thinking and action – it arranges the space of an event. Tschumi’s buildings, defined as folies, in an essential way destabilise any created order, and at the same time they refresh it. Derrida’s statement suggests that architecture may become both metaphor of an order merging a language or a society but also of inner forces which deconstruct and reconstruct it. Therefore architecture is at the same time a construction, a deconstruction and a reconstruction. Parc de la Villette stands out in this system with its attempt to step beyond the scheme of an easy repetition and its heading for chances of achieving more radical otherness. -/- Conclusion Destruction as construction. Paradoxes of deconstruction in architecture -/- Scepticism about persistence and common importance of fundamental values of human culture evinced in philosophers and writers’ works as early as in Greek antiquity, nevertheless it was not expressed so strongly as in the second half of the 20th century. Especially in Heidegger’s work Being and Time (although originated in 1927, still influential in all later philosophy) the following states were characterised: the state of losing the ground (Abgrund), of being out of sight (Unheimlichkeit) and of being out of dwelling (Un-zuhause-sein) – as the basis of self-confidence of conscious being there (Dasein). The entire criticism of philosophy of home and dwelling draws the inspiration from this early writing of the German philosopher, it combines crisis of basic terms of metaphysics with social conditions which are dictated by living in large metropolis. The crisis of both metaphysical foundation and home appears to be similar to the situation of weakening the relations between a man and his dwelling in extensively expanding cities. Whereas philosophy, as well as many disciplines of social sciences, have diagnosed for a long time the destabilisation of fundamental ideas of Western culture and crucial changes in the ways of dwelling, architecture itself occurred to be “the last fortress of metaphysics” (J. Derrida). Among contemporary architects, Peter Eisenman and Bernard Tschumi were the ones who engaged most decidedly in the issues of critical analysis of architecture foundation and its social role. Both the architects noticed new formulas of contemporary social and individual existence, tremendously different from the entire history, and at the same time they affirmed lack of adequacy of architecture concepts to new situations. Both Eisenman and Tschumi used to describe the existing architecture as a tool for consolidation of highly integrated and hierarchised societies, and also as a discipline extremely uncoincidental with the current character of social life based on ideas of freedom and diversity. The means to transform architecture and make a factor of further social changes out of it, was a concept that accentuated revealing the inner contradictions of this discipline, and considering them in designing strategies. Eisenman’s activity, in regard of what has just been noticed, was focused on questioning the basic rules of traditionally comprehended architecture, especially the rule of purpose. The American architect noticed that the concept of architecture as fulfilment the need of location, hides away the fact that the location has to be constantly reconsidered, and hence it is overtaken by change (dislocation). Therefore new concept of architecture propounded architectural activity to translocate the concept of location – more than before – but also to change its status perpetually. Such comprehended architecture should claim, as its main purpose, the constant revision of this purpose and create itself anew permanently. Even Eisenman’s earliest designs of houses nos. I-IV broke with such values as the sense of safety, closeness and familiarity, and just on the contrary they accentuated senses of strangeness, homelessness and loss of confidence. The contradictions within architecture noticed by Tschumi referred to combination of intellectual and sensual values in architecture, when their non-appropriation was defeated by an additional condition, namely the way of experience based on pleasure of excess, marked by insanity. The features of folly were especially visible in his designs of gardens, where the order of planning was mixed with sensual experience introduced by particular elements (both the ones created by nature, and the buildings defined as folies). Parc de la Villette designed by the French architect in Paris put in question not only the common understanding of purpose in architecture but also the ideas of order and integrity, as its plan was based on the combination of independent layers with records of grids of points, various lines and planes. The architecture that collides inadequate elements with each other was supposed to be a kind of an event with no beginning and no end. The architecture treated as an event became a form of a space weakened articulation that maintains its diversity and lack of accordance of the elements building it up. The analyses of Eisenman and Tschumi’s theoretical writings indicate how much the aims of architecture have actually changed; instead of supporting social persistence, the architecture is rather intensifying contradictions, and instead of providing people with the sense of safety, it sublimes danger. From simple acts of defamiliarisation, increasing the distance to itself and enhancing the role of theory, through discomfort, anxiety, not feeling someone at home, weirdness, excess, shock and violence, architecture reached the edge of stability and uncertainty, only to make an attempt at penetrating what is impossible and unutterable, and recording what cannot become the subject of any records. -/- . (shrink)

Interval Temporal Logic is a finite-time linear temporal logic with applications in hardware verification, temporal logic programming and specification of multimedia documents. Due to the logic's non-elementary complexity, efficient ITL-based verification tools have been difficult to develop, even for propositional subsets. MONA is an efficient implementation of an automata-based decision procedure for the logic WS1S. Despite the non-elementary complexity of WS1S, MONA has been successfully applied in problems such as hardware synthesis, protocol verification and theorem proving. Here we consider a (...) rich propositional subset of ITL, PITL, whose expressive power is equivalent to that of WS1S, and in turn to that of regular languages. PITL not only includes operators such as chop, star and projection, but also past operators such as previous, chop in the past and since. We provide an interpretation of PITL formulas in WS1S, which led us to a direct translation from PITL formulas to MONA specifications. We present the tool PITL2MONA as an implementation of such translation. With PITL2MONA acting as a front-end, MONA is used as a decision procedure for PITL. To our knowledge, this is one of the few implementations of a decision procedure for PITL, the first one based on automata, and the only one which handles both projection and past operators. We have tested our implementation on a number of examples; we show in this paper the application of PITL and its MONA-based decision procedure in solutions to the dining-philosophers and a multimedia synchronisation problem, together with some experimental results on these and some other examples. (shrink)

We present an epistemic default logic, based on the metaphore of a meta-level architecture. Upward reflection is formalized by a nonmonotonic entailment relation, based on the objective facts that are either known or unknown at the object level. Then, the meta (monotonic) reasoning process generates a number of default-beliefs of object-level formulas. We extend this framework by proposing a mechanism to reflect these defaults down. Such a reflection is seen as essentially having a temporal flavour: defaults derived at the (...) meta-level are projected as facts in a next object level state. In this way, we obtain temporal models for default reasoning in meta-level formalisms which can be conceived as labeled branching trees. Thus, descending the tree corresponds to shifts in time that model downward reflection, whereas the branching of the tree corresponds to ways of combining possible defaults. All together, this yields an operational or procedural semantics of reasoning by default, which admits one to reason about it by means of branching-time temporal logic. Finally, we define sceptical and credulous entailment relations based on these temporal models and we characterize Reiter extensions in our semantics. (shrink)

The Bentham Project is delighted to announce a call for papers for “Bentham and Australia: Convicts, Utility, and Empire”, a conference to be held at University College London on 11-12 April 2019 to mark the forthcoming publication of Writings on Australia, a volume of The Collected Works of Jeremy Bentham. The conference will explore themes such as the influence and impact of Bentham’s ideas on the theory and practice of punishment in convict Australia, on advocates and opponents of co...

Ritualistic formulae and acts pervade the political, legal, societal and religious life of the ancient world. In many instances there are striking similarities between the formulae of the Greco-Roman world and those of the Near East. Often illumination exists from one to the other. Here I wish to notice a few passages in Greek drama where I think such illumination is possible.

Praise for Volume 1: "... a first-rate edition, which supersedes all other portable Peirces.... all the Peirce most people will ever need." —Louis Menand, The New York Review of Books Volume 2 of this convenient two-volume chronological reader’s edition provides the first comprehensive anthology of the brilliant American thinker Charles Sanders Peirce’s mature philosophy. A central focus of Volume 2 is Peirce’s evolving theory of signs and its appplication to his pragmatism.

Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This equality is motivated by generality of deductions. Characterizations are given for pairs of isomorphic formulae, which lead to decision procedures for this isomorphism.

Ancient Greek mathematics developed the original feature of being deductive mathematics. This article attempts to give a explanation f or this achievement. The focus is on the use of a fixed system of linguistic formulae in Greek mathematical texts. It is shown that the structure of this system was especially adapted for the easy computation of operations of substitution on such formulae, that is, of replacing one element in a fixed formula by another, and it is further argued that such (...) operations of substitution were the main logical tool required by Greek mathematical deduction. The conclusion explains why, assuming the validity of the description above, this historical level is the best explanatory level for the phenomenon of Greek mathematical deduction. (shrink)

Volume 8 of this landmark edition follows Peirce from May 1890 through July 1892—a period of turmoil as his career unraveled at the U.S. Coast and Geodetic Survey. The loss of his principal source of income meant the beginning of permanent penury and a lifelong struggle to find gainful employment. His key achievement during these years is his celebrated Monist metaphysical project, which consists of five classic articles on evolutionary cosmology. Also included are reviews and essays from The Nation in (...) which Peirce critiques Paul Carus, William James, Auguste Comte, Cesare Lombroso, and Karl Pearson, and takes part in a famous dispute between Francis E. Abbot and Josiah Royce. Peirce's short philosophical essays, studies in non-Euclidean geometry and number theory, and his only known experiment in prose fiction complete his production during these years. Peirce's 1883-1909 contributions to the Century Dictionary form the content of volume 7 which is forthcoming. (shrink)