In this paper we start an investigation of a logic called the logic of algebraic rules. The relation of derivability of this logic is defined on universal closures of special disjunctions of equations extending the relation of derivability of the usual equational logic. The paper contains some simple theorems and examples given in justification for the introduction of our logic. A number of open questions is posed.
The paper is a critical reaction to Marcin Trepczyński article “Thomas Aquinas Non-Monotonically” (Filozofia Nauki 2/2011). It is shown that the author misunderstood the real forms of Thomas Aquinas reasoning. I present arguments which show why these reasonings are monotonic by analyzing some of the examples which Trepczyński is using to justify the opposite thesis.
Non-monotonic logics has been popular for recent 15 years. However, it occurs that they are useful to describe some reasonings presented by… Thomas Aquinas. In this paper I show four examples of reasonings where Thomas abandons the principle of monotonicity, all taken from two questions of Summa theologiae concerning God. In each of them Aquinas adds some new premises to the previous set of premises and then draws a conclusion contrary to the previous one, what is impossible under the classical (...) inference. In the next step I present some conclusions, primarily: that for sure we cannot state that these reasonings are just entimematic; that Thomas appears as a superintelligent observer having a holistic view and hence may seem to use in his reasonings rather reduction than deduction; and that we should not call his logic „default”, but rather talk about „the logic of theoria ” or „contemplative/speculative logic”. Finally, I try to find the goal (or the meaning) of using by Thomas one of non-monotonic logics, taking into account that his inferential and interpretive rules serve to organise and clarify some theses (which are very instructive from the perspective of hermeneutics). Perhaps we may find this goal in… education. Well, after all, the Summa is a textbook. As we can see — not only of theology. (shrink)
Fr. Tomasz Czernik Charles Taylor’s Concept of Self-identitySelf-identity, according to Charles Taylor, comes from the community, especially through intersubjective communication. Self-awareness develops from contact with other people. The subject enters this way a moral dimension and public space. On this basis, he can talk about himself because he can describe himself in a social context. The self-identity is represented and conditioned over time. Its stability is rooted in social cohesion, which is based on culture. In the absence of such (...) consistency, there is a modernist and romantic tendency in society. Keywords: Self-identity, Charles Taylor, society, community. (shrink)
Author: Kupś Tomasz Title: ELEMENTS OF TRANSCENDENTAL THEOLOGY IN THE PHILOSOPHY OF RELIGION OF IMMANUEL KANT (Elementy teologii transcendentalnej w filozofii religii Immanuela Kanta) Source: Filo-Sofija year: 2005, vol:.5, number: 2005/1, pages: 91-103 Keywords: TRANSCENDENTAL THEOLOGY, PHILOSOPHY OF RELIGION, KANT Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail: www:In Kantian philosophical system transcendental theology is a part of cognition of pre-being educed only from transcendental notions. Nevertheless any attempts of speculative cognition of (...) pre-being are futile. The value of the transcendental theology is thus merely negative as it shows the bounds of theoretical use of the reason. The idea of the pre-being gains its reality only in the practical use of the reason. In this way transcendental theology becomes the first premise of religion. (shrink)
Author: Kupś Tomasz Title: IMMANUEL KANT’S EXPLANATION OF THE TEXT OF THE BIBLE (Immanuela Kanta wykładnia tekstu Biblii) Source: Filo-Sofija year: 2006, vol:.6, number: 2006/1, pages: 59-70 Keywords: KANT, BIBLE, SCRIPTURE, HISTORICAL RECONSTRUCTION Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail: www:The article consists of two parts. The first is the historical reconstruction of the fortunes of Kant’s private copy of the Scripture. The book was lost during the Second World War and (...) the information about Kant’s notes made on its margins come only from commentators’ studies. The second part contains a short comparison of the main assumptions and rules of moral interpretation of the Scripture’s text. The rules can be traced in two works of Kant: Religion Within the Limits of Reason Alone and The Conflicts of the Faculties. (shrink)
Author: Mróz Tomasz Title: TWO IMAGES OF PLATO IN THE WORKS OF WŁADYSŁAW TATARKIEWICZ (Dwa wizerunki Platona w twórczości Władysława Tatarkiewicza) Source: Filo-Sofija year: 2011, vol:.13/14, number: 2011/2-3, pages: 535-557 Keywords: WŁADYSŁAW TATARKIEWICZ, PLATO, NEO-KANTIAN, PAUL NATORP, RECEPTION OF THE PLATO IN POLAND, THE HISTORY OF PHILOSOPHY IN THE 20TH CENTURY Discipline: PHILOSOPHY Language: POLISH Document type: ARTICLE Publication order reference (Primary author’s office address): E-mail: www:The paper discusses two different approaches of W. Tatarkiewicz to Plato and Platonism. As (...) a former student of the neo-Kantian school in Marburg he shared Paul Natorp’s reading of Plato’s theory of ideas. Tatarkiewicz expressed his agreement with Natorp’s interpretation of the ideas as laws and explanations, in a paper titled A Dispute about Plato (Spór o Platona, 1911). Twenty years later, however, while working on his academic textbook of the history of philosophy, Tatarkiewicz presented Plato’s philosophy in a more balanced manner. In his History of Philosophy two interpretations of the theory of ideas – traditional, Aristotelian and neo-Kantian – were both presented as well-founded. The differences between these two images of Plato in Tatarkiewicz’s works are emphasized. Moreover, some remarks on the reception of the neo-Kantian interpretation of Plato in Poland are presented, as well as the early reaction on the monumental Tatarkiewicz’s History of Philosophy. (shrink)
Św. Tomasz nie napisał nigdy własnego traktatu, w którym wykładałby zasady uprawiania psychologii, podobnie jak nie napisał takiego traktatu odnośnie do innych nauk filozoficznych. Wyjątkiem pozostaje teologia. Pierwsza kwestia, I części Sumy Teologii i piąta oraz szósta kwestia Komentarza do Boecjańskiego dziełka O Trójcy Świętej stanowi bowiem takie traktaty metodologiczne, gdzie Akwinata wyłożył ewidentnie własne poglądy. W przypadku psychologii pozostawił jednak dwie lekcje otwierające Komentarz do Arystotelesowego Traktatu o duszy, w których choć dość literalnie omawia tekst Stagiryty, to formułuje (...) w nim pewien schemat metodologiczny psychologii. Można by sądzić, że przedstawia tam jedynie zawartość komentowanego dzieła, zwłaszcza że styl całej pierwszej części Komentarza jest dość literalny i na pierwszy rzut oka mało znajdujemy tu elementu interpretacyjnego. Uważna analiza pokazuje jednak coś innego. (shrink)
It is argued that recent discussion of the principle of the identity of indiscernibles (PII) and quantum mechanics has lost sight of the broader philosophical motivation and significance of PII and that the `received view' of the status of PII in the light of quantum mechanics survives recent criticisms of it by Muller, Saunders, and Seevinck.
This book contains a concise introduction to one of the most fundamental branches of philosophy, which deals with reality and its nature. Among the topics discussed are such metaphysical questions as "Are we fundamentally free?", "Does time really pass?", "Are there any abstract objects?", "What is causation?", "What are necessary and possible truths?". The book is aimed at absolute beginners, so it does not presuppose any previous knowledge of philosophy from the reader. For those who would like to pursue the (...) subject a bit deeper, the book comes equipped with an extended list of further reading. (shrink)
In the first section of the chapter, I scrutinize Howard Stein’s 1991 definition of a transitive becoming relation that is Lorentz invariant. I argue first that Stein’s analysis gives few clues regarding the required characteristics of the relation complementary to his becoming—i.e. the relation of indefiniteness. It turns out that this relation cannot satisfy the condition of transitivity, and this fact can force us to reconsider the transitivity requirement as applied to the relation of becoming. I argue that the relation (...) of becoming need not be transitive, as long as it satisfies the weaker condition of “cumulativity”: for a given observer the area of the events that have become real should not diminish as time progresses. I show that there are actually two relations of becoming that meet this weakened condition: Stein’s (transitive) relation of causal past connectibility and the (non-transitive) relation that is the logical complement of the future causal connectibility. In the second part of the chapter I defend Stein’s notion of temporal becoming against the attack that appeals to quantum-mechanical non-locality. I critically evaluate the argument given by Mauro Dorato (1996) that purports to show that space-like separated measurements done on the EPR system have to be mutually determinate. Finally, in order to account for the truth of counterfactual statements that link the space-like separated outcomes, I propose a dynamic conception of becoming, according to which the sphere of determinate events as of a given point may depend on the physical phenomena transpiring at this point. (shrink)
We investigate the concepts of past, present, and future that build upon a modal distinction between the settled past and the open future. The concepts are defined in terms of a pre-causal ordering and of qualitative differences between alternative histories. Finally, we look what an event's past, present, and future look like in the so-called Minkowskian Branching Structures, in which histories are isomorphic to Minkowski spacetime.
Several people have helped us to write this essay. Our greatest debt is to Wlodek Rabinowicz, who has been an excellent supervisor of the project. He spent a lot of time and energy reading drafts of the essay. Without his painstaking criticism and helpful comments this essay would lack in precision, relevance, and logical correctness. Earlier drafts of the essay were discussed in Sven Danielsson and Wlodek Rabinowicz's seminar at the Department of Philosophy, University of Uppsala. The participants of the (...) seminar contributed with helpful criticisms. Apart from Sven and Wlodek, we would like to thank Thomas Anderberg, Erik Carlson, Tomasz Pol, Peter Ryman, Rysiek Sliwinski, and Jan Österberg. We are especially grateful to Erik Carlson. His critical eye detected many flaws in earlier versions of our theory. (shrink)
Three basic positions regarding the nature of fundamental properties are: dispositional monism, categorical monism and the mixed view. Dispositional monism apparently involves a regress or circularity, while an unpalatable consequence of categorical monism and the mixed view is that they are committed to quidditism. I discuss Alexander Bird's defence of dispositional monism based on the structuralist approach to identity. I argue that his solution does not help standard dispositional essentialism, as it admits the possibility that two distinct dispositional properties can (...) possess the same stimuli and manifestations. Moreover, Bird's argument can be used to support the mixed view by relieving it of its commitment to quidditism. I briefly analyse an alternative defence of dispositional essentialism based on Leon Horsten's approach to the problem of circularity and impredicativity. I conclude that the best option is to choose Bird's solution but amend the dispositional perspective on properties. According to my proposal, the essences of dispositions are determined not directly by their stimuli and manifestations but by the role each property plays in the structure formed by the stimulus/manifestation relations. (shrink)
This book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the possible-world (...) semantics of quantum counterfactuals using David Lewis's famous approach as a starting point but modifying it significantly in order to achieve compatibility with the demands of the special theory of relativity as well as quantum mechanics. There have been several attempts to use counterfactuals semantics to strengthen Bell's theorem and its cognates such as the GHZ and Hardy theorems. These are critically evaluated in the book. Finally, a counterfactual reconstruction of the EPR argument and Bell's theorem is proposed that sheds a new light on their philosophical consequences regarding the relations between realism and local causation. (shrink)
Konserwatywni przeciwnicy prowadzenia badań naukowych na ludzkich embrionach argumentują, że od momentu poczęcia mają one status moralny równy statusowi ludzi dorosłych: zarodki mają takie samo prawo do życia jak dorośli. W artykule przedstawiam oryginalną argumentację za tym stanowiskiem, której źródła można znaleźć w XVII-wiecznej teologii moralnej i współczesnej teorii decyzji. Argumentacja ta nie odwołuje się do statusu ontologicznego embrionów, ale do pewnego typu rozumowania praktycznego na temat tego, co należy robić w rozmaitych sytuacjach niepewności. Na pierwszy rzut oka wydaje się (...) ona wzmacniać stanowisko konserwatywne, ponieważ nie zależy od kontrowersyjnych metafizycznych założeń na temat statusu zarodków czy kwestii ich potencjalności. W artykule pokażę jednak, że argumentacja ta obarczona jest poważnymi wadami, które sprawiają, że nie da się jej zastosować do uzasadnienia sprzeciwu wobec moralnej czy prawnej dopuszczalności np. badań na zarodkowych komórkach macierzystych. (shrink)
David Lewis’s latest theory of causation defines the causal link in terms of the relation of influence between events. It turns out, however, that one event’s influencing another is neither a necessary nor sufficient condition for its being a cause of that event. In the article one particular case of causality without influence is presented and developed. This case not only serves as a counterexample to Lewis’s influence theory, but also threatens earlier counterfactual analyses of causation by admitting a particularly (...) troublesome type of preemption. The conclusion of the article is that Lewis’s influence method of solving the preemption problem fails, and that we need a new and fresh approach to the cases of redundant causation if we want to hold on to the counterfactual analysis of causation. (shrink)
In the paper, the proof of the non-locality of quantum mechanics, given by Bedford and Stapp (1995), and appealing to the GHZ example, is analyzed. The proof does not contain any explicit assumption of realism, but instead it uses formal methods and techniques of the Lewis calculus of counterfactuals. To ascertain the validity of the proof, a formal semantic model for counterfactuals is constructed. With the help of this model it can be shown that the proof is faulty, because it (...) appeals to the unwarranted principle of “elimination of eliminated conditions” (EEC). As an additional way of showing unreasonableness of the assumption (EEC), it is argued that yet another alleged and highly controversial proof of non-locality of QM, using the Hardy example, can be made almost trivial with the help of (EEC). Finally, a general argument is produced to the effect that the locality condition in the form accepted by Stapp and Bedford is consistent with the quantum-mechanical predictions for the GHZ case under the assumption of indeterminism. This result undermines any future attempts of proving the incompatibility between the predictions of quantum theory and the idea of no faster-than-light influence in the GHZ case, quite independently of the negative assessment of the particular derivation proposed by Stapp and Bedford. (shrink)
In the article the possibility of breaking the eigenvalue-eigenstate link in quantum mechanics is considered. An argument is presented to the effect that there are some non-maximal observables for which the implication from eigenstates to eigenvalues is not valid, i.e. such that although the probability of revealing certain value upon measurement is one, they don't possess this value before the measurement. It is shown that the existence of such observables leads to contextuality, i.e. the thesis that one Hermitean operator can (...) represent more than one physical observable. Finally, contextuality brought about by these considerations is compared with contextuality suggested by the Kochen-Specker paradox. (shrink)
General metaphysical arguments have been proposed in favour of the thesis that all dispositions have categorical bases (Armstrong; Prior, Pargetter, Jackson). These arguments have been countered by equally general arguments in support of ungrounded dispositions (Molnar, Mumford). I believe that this controversy cannot be settled purely on the level of abstract metaphysical considerations. Instead, I propose to look for ungrounded dispositions in specific physical theories, such as quantum mechanics. I explain why non-classical properties such as spin are best interpreted as (...) irreducible dispositional properties, and I give reasons why even seemingly classical properties, for instance position or momentum, should receive a similar treatment when interpreted in the quantum realm. Contrary to the conventional wisdom, I argue that quantum dispositions should not be limited to probabilistic dispositions (propensities) by showing reasons why even possession of well-defined values of parameters should qualify as a dispositional property. I finally discuss the issue of the actuality of quantum dispositions, arguing that it may be justified to treat them as potentialities whose being has a lesser degree of reality than that of classical categorical properties, due to the incompatibility relations between non-commuting observables. (shrink)
The article presents a formalization of Anselm's so-called Ontological Arguments from Proslogion . The main idea of our research is to stay to the original text as close as is possible. We show, against some common opinions, that (i) the logic necessary for the formalization must be neither a purely sentential modal calculus, nor just non-modal first-order logic, but a modal first-order theory; (ii) such logic cannot contain logical axiom ⌜ A → ⋄ A ⌝; (iii) none of Anselm's reasonings (...) requires the assumptions that God is a consistent object or that existence of God is possible (in symbols "⋄Eg"); (iv) no such thing as the so-called Anselm's Principle (in symbols "□(Eg → □Eg)") is involved in any of the proofs; (v) Anselm's claims (that God exists in reality and that God necessarily exists in reality) can be obtained independently, hence there is no need for presenting them in an opposite order than Anselm did. Moreover we show a single line of reasoning underlying the whole Proslogion and allowing Anselm to deduce many theorems concerning God's nature. Last but not least we study the possibility of proving the uniqueness of God within the outlined theory. (shrink)
The paper consists of two parts. The first part begins with the problem of whether the original three-valued calculus, invented by J. Łukasiewicz, really conforms to his philosophical and semantic intuitions. I claim that one of the basic semantic assumptions underlying Łukasiewicz's three-valued logic should be that if under any possible circumstances a sentence of the form "X will be the case at time t" is true (resp. false) at time t, then this sentence must be already true (resp. false) (...) at present. However, it is easy to see that this principle is violated in Lukasiewicz's original calculus (as the cases of the law of excluded middle and the law of contradiction show). Nevertheless it is possible to construct (either with the help of the notion of "supervaluation", or purely algebraically) a different three-valued, semi-classical sentential calculus, which would properly incorporate Łukasiewicz's initial intuitions. Algebraically, this calculus has the ordinary Boolean structure, and therefore it retains all classically valid formulas. Yet because possible valuations are no longer represented by ultrafilters, but by filters (not necessarily maximal), the new calculus displays certain non-classical metalogical features (like, for example, nonextensionality and the lack of the metalogical rule enabling one to derive "p is true or q is true" from" 'p ∨ q' is true"). The second part analyses whether the proposed calculus could be useful in formalizing inferences in situations, when for some reason (epistemological or ontological) our knowledge of certain facts is subject to limitation. Special attention should be paid to the possibility of employing this calculus to the case of quantum mechanics. I am going to compare it with standard non-Boolean quantum logic (in the Jauch-Piron approach), and to show that certain shortcomings of the latter can be avoided in the former. For example, I will argue that in order to properly account for quantum features of microphysics, we do not need to drop the law of distributivity. Also the idea of "reading off" the logical structure of propositions from the structure of Hilbert space leads to some conceptual troubles, which I am going to point out. The thesis of the paper is that all we need to speak about quantum reality can be acquired by dropping the principle of bivalence and extensionality, while accepting all classically valid formulas. (shrink)
In this paper we examine Prior’s reconstruction of Master Argument  in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K t 4 plus a new axiom ( P ): ‘ p Λ G p ⊃ P G p ’. This formula was used by Prior in his original analysis of Master Argument. ( P ) (...) is usually added as an extra axiom to an axiomatization of the logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by ( P ) in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction. (shrink)
The article deals with one particular problem created by the counterfactual analysis of causality à la Lewis, namely the context-sensitivity problem or, as I prefer to call it, the background condition problem. It appears that Lewis’ counterfactual definition of causality cannot distinguish between proper causes and mere causal conditions – i.e. factors necessary for the effect to occur, but commonly not seen as causally efficacious. The proposal is put forward to amend the Lewis definition with a condition, based on the (...) notion of cotenability, which would eliminate the problem. It is shown that the corrected definition of causality leads to the transitivity of the causal relation. Possible objections to the proposed solution, involving the assumption of indeterminism and the preemption cases, are given a thorough consideration. (shrink)