In this paper, we focus on the development of geometric cognition. We argue that to understand how geometric cognition has been constituted, one must appreciate not only individual cognitive factors, such as phylogenetically ancient and ontogenetically early core cognitive systems, but also the social history of the spread and use of cognitive artifacts. In particular, we show that the development of Greek mathematics, enshrined in Euclid’s Elements, was driven by the use of two tightly intertwined cognitive artifacts: the use of (...) lettered diagrams; and the creation of linguistic formulae. Together, these artifacts formed the professional language of geometry. In this respect, the case of Greek geometry clearly shows that explanations of geometric reasoning have to go beyond the confines of methodological individualism to account for how the distributed practice of artifact use has stabilized over time. This practice, as we suggest, has also contributed heavily to the understanding of what mathematical proof is; classically, it has been assumed that proofs are not merely deductively correct but also remain invariant over various individuals sharing the same cognitive practice. Cognitive artifacts in Greek geometry constrained the repertoire of admissible inferential operations, which made these proofs inter-subjectively testable and compelling. By focusing on the cognitive operations on artifacts, we also stress that mental mechanisms that contribute to these operations are still poorly understood, in contrast to those mechanisms which drive symbolic logical inference. (shrink)

A pigeon has been conditioned to peck at red objects and has also been conditioned to peck at triangular objects. The pigeon is now presented with a red triangle and pecks. In virtue of which of the object's properties did the pigeon peck? I argue that the disjunctive property "red or triangular" best answers this question and that this in turn gives us reason to admit such disjunctive properties to our ontology. I also show how the criterion for causal efficacy (...) that I employ, expressed in terms of counterfactual conditionals, works to preclude spurious disjunctive properties from counting as efficacious. (shrink)

One of the logic defined by Richard Epstein in a context of an analysis of subject matter relationship is Symmetric Relatedness Logic S. In the monograph [2] we can find some open problems concerning relatedness logic, a Post-style completeness theorem for logic S is one of them. Our paper introduces a solution of this metalogical issue.

The current paper studies the formal properties of the Global Reflection Principle, to wit the assertion “All theorems of$\mathrm {Th}$are true,” where$\mathrm {Th}$is a theory in the language of arithmetic and the truth predicate satisfies the usual Tarskian inductive conditions for formulae in the language of arithmetic. We fix the gap in Kotlarski’s proof from [15], showing that the Global Reflection Principle for Peano Arithmetic is provable in the theory of compositional truth with bounded induction only ($\mathrm {CT}_0$). Furthermore, we (...) extend the above result showing that$\Sigma _1$-uniform reflection over a theory of uniform Tarski biconditionals ($\mathrm {UTB}^-$) is provable in$\mathrm {CT}_0$, thus answering the question of Beklemishev and Pakhomov [2]. Finally, we introduce the notion of a prolongable satisfaction class and use it to study the structure of models of$\mathrm {CT}_0$. In particular, we provide a new model-theoretical characterization of theories of finite iterations of uniform reflection and present a new proof characterizing the arithmetical consequences of$\mathrm {CT}_0$. (shrink)

One criticism of David Lewis's account of counterfactuals is that it sometimes assigns the wrong truth-value to a counterfactual when both antecedent and consequent happen to be true. Lewis has suggested a possible remedy to this situation, but commentators have found this to be unsatisfactory. I suggest an alternative solution which involves a modification of Lewis's truth conditions, but which confines itself to the resources already present in his account. This modification involves the device of embedding one counterfactual within another. (...) On the revised set of truth conditions, counterfactuals with true components are sometimes true and sometimes false, in a way that is more in keeping with our intuitive judgments about such statements. (shrink)

In consequence of significant social, political, economic, and demographic changes several wildlife species are currently growing in numbers and recolonizing Europe. While this is rightly hailed as a success of the environmental movement, the return of wildlife brings its own issues. As the animals arrive in the places we inhabit, we are learning anew that life with wild nature is not easy, especially when the accumulated cultural knowledge and experience pertaining to such coexistence have been all but lost. This book (...) provides a hermeneutic study of the ways we come to understand the troubling impacts of wildlife by exploring and critically discussing the meanings of 'ecological discomforts'. Thus, it begins the work of rebuilding the culture of coexistence. The cases presented in this book range from crocodile attacks to mice infestations, and their analysis consequently builds up an ethics that sees wildlife as active participants in the shaping of human moral and existential reality. This book is of interest not only to environmental philosophers, who will find here an original contribution to the established ethical discussions, but also to wildlife managers, and even to those members of the public who themselves struggle to make sense of encounters with their new wild neighbors. (shrink)

The main purpose of the paper is to develop a concept of _model uncertainty_ as opposed to the existing and well-established concept of model risk. Up to date the broad literature on probability not only developed complete probability systems, but also correctly noticed limitations of probability calculus. Despite the acknowledgement of such probability restrictions, drawbacks of modeling are often related to model risk. We present an argument here to distinguish a feature limiting models even further: model uncertainty. The tenets of (...) it already exist in the literature on probability, but were not properly emphasized while the idea of model risk was developed. Our plan it to start with a broad overview of the existing knowledge about probability in order to start with fundamental principles. From them we are deriving a new concept of model uncertainty. (shrink)

This paper outlines various classroom exercises to be given at the beginning of an introductory logic course. The purpose of the exercises is to gain students’ attention while introducing them to basic terms and principles of logic, both inductive and deductive. The suggested exercises are flexible enough to introduce a range of material and to do so in a variety of sequences, according to the instructor’s preference.

Temporal logic of causal knowledge over general partially ordered structures of local states is defined. The definition of knowledge captures the change of state due to action executions. The structures are a variant of flow event structures including prime event structures and branching processes of Petri Nets. Modalities corresponding to the causality, concurrency, and indistinguishability relations are used. Formulas are interpreted over local state occurrences. The logic is proved to be decidable and a complete axiomatization is provided.

The book Metaphysics by Tomasz Bigaj is intended to be an introduction to the basic issues of analytical metaphysics designed for non-philosophers. It fulfills its purpose to a large extent: the issues are competently presented in a clear and accessible way, even when referring to a very complex subjects. The unquestionable advantage of the book is also the fact that it indicates a strong relation between philosophical problems and those of other scientific disciplines, mainly physics and mathematics. It makes Bigaj’s (...) work an attractive handbook for the laymen as well as for professionals in other fields. (shrink)

A method of constructing Hilbert-type axiom systems for standard many-valued propositional logics was offered by Rosser and Turquette. Although this method is considered to be a solution of the problem of axiomatisability of a wide class of many-valued logics, the article demonstrates that it fails to produce adequate axiom systems. The article concerns finitely many-valued propositional logics of Łukasiewicz. It proves that if standard propositional connectives of the Rosser–Turquette axiom systems are definable in terms of the propositional connectives of Łukasiewicz’s (...) logics, and thus, they are normal ones, then every Rosser–Turquette axiom system for a finite-valued Łukasiewicz’s logic is semantically incomplete. (shrink)

The notion of implicit commitment has played a prominent role in recent works in logic and philosophy of mathematics. Although implicit commitment is often associated with highly technical studies, it remains an elusive notion. In particular, it is often claimed that the acceptance of a mathematical theory implicitly commits one to the acceptance of a Uniform Reflection Principle for it. However, philosophers agree that a satisfactory analysis of the transition from a theory to its reflection principle is still lacking. We (...) provide an axiomatization of the minimal commitments implicit in the acceptance of a mathematical theory. The theory entails that the Uniform Reflection Principle is part of one’s implicit commitments, and sheds light on why this is so. We argue that the theory has significant epistemological consequences in that it explains how justified belief in the axioms of a theory can be preserved to the corresponding reflection principle. The theory also improves on recent analyses of implicit commitment based on truth or epistemic notions. (shrink)

Boolean connexive logic is an extension of Boolean logic that is closed under Modus Ponens and contains Aristotle’s and Boethius’ theses. According to these theses a sentence cannot imply its negation and the negation of a sentence cannot imply the sentence; and if the antecedent implies the consequent, then the antecedent cannot imply the negation of the consequent and if the antecedent implies the negation of the consequent, then the antecedent cannot imply the consequent. Such a logic was first introduced (...) by Jarmużek and Malinowski, by means of so-called relating semantics and tableau systems. Subsequently its modal extension was determined by means of the combination of possible-worlds semantics and relating semantics. In the following article we present axiomatic systems of some basic and modal Boolean connexive logics. Proofs of completeness will be carried out using canonical models defined with respect to maximal consistent sets. (shrink)

We introduce a principle of local collection for compositional truth predicates and show that it is arithmetically conservative over the classically compositional theory of truth. This axiom states that upon restriction to formulae of any syntactic complexity, the resulting predicate satisfies full collection. In particular, arguments using collection for the truth predicate applied to sentences occurring in any given (code of a) proof do not suffice to show that the conclusion of that proof is true, in stark contrast to the (...) case of the induction scheme. We analyse various further results concerning end-extensions of models of compositional truth and the collection scheme for the compositional truth predicate. (shrink)

This paper is a follow-up to [4], in which a mistake in [6] (which spread also to [9]) was corrected. We give a strenghtening of the main result on the semantical nonconservativity of the theory of PT−with internal induction for total formulae${(\rm{P}}{{\rm{T}}^ - } + {\rm{INT}}\left( {{\rm{tot}}} \right)$, denoted by PT−in [9]). We show that if to PT−the axiom of internal induction forallarithmetical formulae is added (giving${\rm{P}}{{\rm{T}}^ - } + {\rm{INT}}$), then this theory is semantically stronger than${\rm{P}}{{\rm{T}}^ - } + (...) {\rm{INT}}\left( {{\rm{tot}}} \right)$. In particular the latter is not relatively truth definable (in the sense of [11]) in the former. Last but not least, we provide an axiomatic theory of truth which meets the requirements put forward by Fischer and Horsten in [9]. The truth theory we define is based on Weak Kleene Logic instead of the Strong one. (shrink)

Idea słowiańska” jest terminem ogólnym, odnoszącym się do wielu politycznych, historiozoficznych i kulturowych wątków, dla których inspiracją było językowe i kulturowe pokrewieństwo między narodami słowiańskimi. Takie ruchy jak słowianofilstwo i panslawizm miały na celu kulturalne i polityczne zjednoczenie Słowian. Idea ta wywarła silny wpływ na muzykę krajów środkowej i wschodniej Europy w XIX i XX wieku. Pod jej wpływem powstała znaczna liczba utworów muzycznych. Można utwory te podzielić na kilka grup. W jednych „słowiańskość” podkreślana była poprzez tytuł. Kompozytorzy używali również (...) typowo słowiańskich gatunków tanecznych i pieśniowych, jak polski mazurek i ukraińska dumka. Innym sposobem realizacji idei słowiańskiej były muzyczne kontakty między twórcami. Idea muzyki słowiańskiej pojawia się również w komentarzach muzykologicznych: słowiański „charakter” muzyczny bywał najczęściej łączony ze specyficznymi kategoriami emocjonalnymi, takimi jak smutek, tęsknota, szczególnie zaś żal, które to określenie stosowano do opisu przemożnego nastroju panującego w dziełach Chopina. (shrink)

This text reviews David Megger’s 2021 book entitled _Justice in Welfare Economics. __Libertarianism and the Austrian School_ (in Polish: _Sprawiedliwość w ekonomii dobrobytu, liberatarianizm i szkoła austriacka_). The review takes a critical approach, highlighting the most significant aspects of the presented considerations and emphasising their uniqueness and complexity. I intend to extensively discuss the author’s theses concerning the modification of the fundamental claims of Austrian school representatives about justice and welfare, highlighting both their strengths and weaknesses.

-/- Medytacje filozoficzne, Fundacja na Rzecz Myślenia im. Barbary Skargi, Warszawa 2015. -/- Publikacja współfinansowana przez Muzeum Łazienki Królewskie w Warszawie. -/- Zbiór tekstów powstałych na podstawie wykładów, które zostały wygłoszone w ramach cyklu "Medytacje filozoficzne w Łazienkach" w latach 2013-2015. -/- -/- Spis treści: -/- Cezary Wodziński, Premedytacja Krzysztof Pomian, O wyjątkowości człowieka Zygmunt Bauman, O miłości i nienawiści… Tropami Barbary Skargi Tadeusz Sławek, Ciemne liturgie. Język, historia i gest błogosławieństwa Lech Witkowski, Rozprawa z autorytetem: w strone autorytu przejścia (...) Władysław Stróżewski, Doświadczenie czasu, doświadczenie istnienia Juliusz Domański, „Pradawna waśń filozofów z poetami” a kłopoty z dziedzictwem antycznym Serhij Żadan, Wolność jako odpowiedzialność Marcin Poręba, Co to jest rzeczywistość? Szymon Wróbel, Co to jest historia filozofii? Magdalena Środa, Moralność życia publicznego Kostiantyn Tyszczenko, Po co językoznawstwu metateoria? (shrink)

ObjectiveThe study aimed to assess the level of disease acceptance as well as the wellbeing and emotions that accompany cancer patients during the COVID-19 pandemic.Materials and MethodsThe study involved 1,000 patients of the oncology centers. The following questionnaires were used for the study: WHO-5–Well-Being Index, BDI–Beck Depression Inventory, disease acceptance scale, and proprietary multiple-choice questions regarding the impact of the epidemic situation on the respondents’ lives so far. The questionnaire study was conducted twice: in March-October 2020 and March-October 2021. The (...) differences between the given periods were statistically analyzed.ResultsAt the time of the study, the respondents felt mainly anxiety related to the possibility of contracting COVID-19, the possibility of infecting a loved one, or staying in quarantine. Anxiety was also caused by the vision of poorer access to health services. Along with the duration of the epidemic, the acceptance of neoplastic disease has decreased and the incidence of depressive symptoms has increased.ConclusionThe wellbeing of the respondents deteriorated significantly during the pandemic. The respondents, in their daily functioning, were mainly accompanied by anxiety. The risk of depression has increased and the acceptance of the disease has decreased significantly. (shrink)

Branching is a set-theoretical model of reality that is in accord with contemporary physics. This structure is also a model for some logical calculi. However, if the formal language defined on the basis of branching is to correspond to our ways of speaking about possible events, a number of issues must be clarified. All of them are connected with the notion of possibility that is employed in this language. Yet the apparent need to supplement this language with an additional notion (...) of possibility means that branching ceases to be attractive as a candidate for a model of physical reality, as it contains considerably more elements than we would like to see in reality. Thus, the connection between this logical tool and ontology becomes questionable. (shrink)

This paper discusses main issues concerning Toulmin’s theory of evolutionary development of scientific knowledge. The reconstruction of Toulmin’s assumptions, which underlie the theory, and the presentation of the theory itself, is followed by the analysis of the difficulties of the conception in general. The author tries to show that these difficulties consist primarily in the discrepancy between what Toulmin aimed at and what he actually achieved. The problem is that although incorporating the means of Darwin’s theory may itself be — (...) in the context of describing the growth of scientifi c knowledge — justifi able, it is not consistent with Toulmin’s demand for the rationality of science. The purpose of creating the evolutionary theory was, as Toulmin claimed, to give an account of the development of scientific knowledge which would be non-relativistic and rationalistic. However, this purpose is, as the author argues, not achievable on the grounds of Toulmin’s accounts of rationality. Key words S. TOULMIN, SCIENCE, EVOLUTION. (shrink)

This book aims to present trompe-l'oeil painting as an ambigous aesthetic ideal offered by early modern theory of art. It embodies the idea of an image identical to what it represents. It is interpreted in terms of perceptual and aesthetic illusion, mimesis, diegesis, play, irony and scientific illustration.

This paper aims to shed light on the putative functions of placing images in judicial opinions from the judges’ perspective. Thus far, commentators have overlooked the functions that images play for judges when used in judicial opinions and consequently have failed to provide a thorough understanding of the process. To help fill this gap, Jerome Frank’s ideas on judging will be presented. The argument goes that using images in judicial opinions can be interpreted as a way to enable the decision-making (...) process to be, as far as possible, devoid of hypocrisy, closer to judicial candor and more open to scrutiny. This notion can be excavated from Frank’s works in light of the existential features of both passing judgments and articulating decision-making processes by and for judges themselves. As will be shown, Frank’s views on judicial decision-making are more original and enlightening than critics might suggest and they are particularly relevant when examining the use of images in judicial opinions from a judge’s perspective. (shrink)

The aim of this article is to suggest that one should think of gardens in terms of performances and not necessarily in terms of architecture, painting, or poetry, for it is possible to show that, strangely enough, gardens seem to share certain features with performance arts. Such an approach seems fruitful since it allows one both to grasp the fact that gardens combine culture and nature and to underline the role of the latter, which cannot be reduced to a sheer (...) medium as is traditionally done. The contention is that gardens should be treated more like a continuous, dynamic, partly planned process in which people can participate in different ways on a par with other non-human ‘actors’. Moreover, the category of performance seems to offer a useful framework helping to solve certain problems inherent in traditional ways of thinking about gardens. (shrink)

In the following paper we propose a model-theoretical way of comparing the “strength” of various truth theories which are conservative over $$ PA $$. Let $${\mathfrak {Th}}$$ denote the class of models of $$ PA $$ which admit an expansion to a model of theory $${ Th}$$. We show (combining some well known results and original ideas) that $$\begin{aligned} {{\mathfrak {PA}}}\supset {\mathfrak {TB}}\supset {{\mathfrak {RS}}}\supset {\mathfrak {UTB}}\supseteq \mathfrak {CT^-}, \end{aligned}$$ where $${\mathfrak {PA}}$$ denotes simply the class of all models of (...) $$ PA $$ and $${\mathfrak {RS}}$$ denotes the class of recursively saturated models of $$ PA $$. Our main original result is that every model of $$ PA $$ which admits an expansion to a model of $$ CT ^-$$, admits also an expansion to a model of $$ UTB $$. Moreover, as a corollary to one of the results (brought to us by Carlo Nicolai) we conclude that $$ UTB $$ is not relatively interpretable in $$ TB $$, thus answering the question from Fujimoto (Bull Symb Log 16:305–344, 2010). (shrink)

The book presents a critical overview of Peirce's views on modern nominalism and offers a novel approach to the social-anthropological underpinnings of his realism, especially Pragmatic Realism vis à vis the individualist tendencies in modern thought.

The aim of the paper is to discuss the idea of dialogue with nature. Even though the idea of dialogue with animals, plants – even objects of inanimate nature – is well known, it has usually been treated as an expression of a naive or folk view. Yet, it has recently gained in importance as an idea that is used to describe an ecological approach to natural environment and tends to be treated as a foundation for an ecological culture. A (...) noteworthy contribution to the reconsideration of the concept of human-nature dialogue has also been given by a number of contemporary philosophers who have offered an environmental reinterpretation of phenomenology and hermeneutics based on, among other things, Martin Buber’s concept of the I-You relationship. The paper will focus on two aspects of the concept of dialogue, namely on its epistemological and ethical implications. Following Erazim Kohák’s theory, which will be presented as a key figure of a particular manner of speaking about nature, one that leads to ecological personalism. (shrink)

In this paper, we investigate abstract model-theoretic properties which hold for models in which a truth or satisfaction predicate for a sublanguage of the signature is definable. We analyze in which cases those properties in fact ensure the definability of the respective truth predicate. In some cases, we formulate different axiomatic theories which are indispensable for such properties to hold and we analyze the mutual definability relations between those theories.

Artykuł zawiera analizę wykorzystania kategorii afordancji w koncepcjach socjologicznych, podejmujących problematykę relacji pomiędzy strukturą społeczną a jednostkowym sprawstwem. W tekście skoncentrowano się na dwóch koncepcjach, które stanowią próbę ujęcia tej relacji w spójnym podejściu teoretycznym i bez popadania w skrajny determinizm społeczny oraz nadmierny indywidualizm. Są nimi krytyczny realizm i koncepcja habitusu Pierre’a Bourdieu. Kategoria afordancji jest przedstawiona w artykule jako użyteczne narzędzie do opisu relacji między podmiotem a środowiskiem, które to narzędzie pozwala zwrócić uwagę na czynnik materialny w badaniu (...) struktur społecznych, przy jednoczesnym uznaniu aktywnej roli podmiotu w ich współtworzeniu. Szczególnie obiecujące jest tu osadzenie afordancji w koncepcji poznania rozproszonego, wykorzystywanej w socjologii do badania tzw. struktur socjotechnicznych. ----------------------------------------- Zgłoszono: 30/04/2023. Zrecenzowano: 15/02/2024. Zaakceptowano do publikacji: 24/04/2024. (shrink)