Trzy metody analizy filozoficznej

Niniejsze sprawozdanie jest omówieniem trzech dzieł należących do różnych nurtów. filozofii analitycznej. Bogactwo ujęć składających się na treść tych książek inspiruje do bardziej ogólnych refleksji na temat metod filozofii analitycznej. Refleksjom tym będzie poświęcony końcowy fragment komunikatu, następujący po części sprawozdawczej.     

Normalization and excluded middle. I

The usual rule used to obtain natural deduction formulations of classical logic from intuitionistic logic, namely is stronger then necessary, and will give classical logic when added to minimal logic. A rule which is precisely strong enough to give classical logic from intuitionistic logic, and which is thus exactly equivalent to the law of the excluded middle, is It is a special case of a version of Peirce's law: In this paper it is shown how to normalize logics defined using these last two rules. Part I deals with propositional logics and first order predicate logics. Part II will deal with first order arithmetic and second order logics. This research was supported in part by grants EQ1648, EQ2908, and CE 110 of the program Fonds pour la Formation de Chercheurs et l'aide à la Recherche (F.C.A.R.) of the Quèbec Ministry of Education.     

О Понятии категоричности

Streszczenie Pojęcie kategoryczności zostało wprowadzone w początku obecnego wieku, ażeby scharakteryzować teorie, które w intencji ich twórców mają dokładnie jeden model. Dalszy rozwój badań metalogicznych dotyczących modeli doprowadził do spostrezeżenia, że każda teoria matematyczna opisująca pewien model nieskończony, opisuje równocześnie wiele innych modeli z nim nieizomorficznych. Stąd pierwotne pojęcie kategoryczności straciło na znaczeniu. Pojawiły się natomiast badania mające na celu pewne zmodyfikowanie tego pojęcia. Praca niniejsza omawia różne rodzaje pojęcia kategoryczności znane z literatury logicznej i proponuje pewne nowe.     

The uniqueness of the fixed-point in every diagonalizable algebra

Summary It is well known that, in Peano arithmetic, there exists a formulaTheor (x) which numerates the set of theorems. By Gödel's and Löb's results, we have that Therefore, the considered «equations» admit, up to provable equivalence, only one solution.In this paper we prove (Corollary 1), that, in general, ifP (x) is an arbitrary formula built fromTheor (x), then the fixed-point ofP (x) (which exists by the diagonalization lemma) is unique up to provable equivalence. This result is settled referring to the concept of diagonalizable algebra (see Introduction).The algebraization of the theories which express TheorAllatum est die 3 Augustii 1975     

Familiarity and pop-out in visual search

In this paper, we report that when the low-level features of targets and distractors are held constant, visual search performance can be strongly influenced by familiarity. In the first condition, a was the target amid as distractors, and vice versa. The response time increased steeply as a function of number of distractors (82 msec/item). When the same stimuli were rotated by 90° (the second condition), however, they became familiar patterns— and —and gave rise to much shallower search functions (31 msec/item). In the third condition, when the search was for a familiar target, (or ), among unfamiliar distractors, (or ), the slope was about 46 msec/item. In the last condition, when the search was for an unfamiliar target, (or ), among familiar distractors, s (or s), parallel search functions were found with a slope of about 1.5 msec/item. These results show that familiarity speeds visual search and that it does so principally when the distractors, not the targets, are familiar.     

Twierdzenia o dedukcji niewprost

Przy pisaniu tego artykułu korzystałem z niezmiernie życzliwych i istotnych wskazówek i pomocy Pana Doc. drWitolda A. Pogorzelskiego. Poczuwam się w tym miejscu do miłego obowiązku złożenia Mu serdecznego podziękowania. Allatum est die 9 Januarii 1966     

O klasach normalnych i nienormalnych na terenie języka potocznego

Problematyka i glówne tezy tej pracy pochodz od pierwszego autora. Udzial drugiego autora sprowadza sie do propozycji utosamienia jeezyka potocznego z formalizmem logiki zda i logiki nazw oraz do pewnych sugestii odnonie systematyzacji materialuAllatum est die 2 Octobris 1965     

The impossibility of a bivalent truth-functional semantics for the non-Boolean propositional structures of quantum mechanics

Summary The general fact of the impossibility of a bivalent, truth-functional semantics for the propositional structures determined by quantum mechanics should be more subtly demarcated according to whether the structures are taken to be orthomodular latticesP _L or partial-Boolean algebrasP _A; according to whether the semantic mappings are required to be truth-functional or truth-functional ; and according to whether two-or-higher dimensional Hilbert spaceP structures or three-or-higher dimensional Hilbert spaceP structures are being considered. If the quantumP structures are taken to be orthomodular latticesP _L, then bivalent mappings which preserve the operations and relations of aP _L must be truth-functional . Then as suggested by von Neumann and Jauch-Piron and as proven in this paper, the mere presence of incompatible elements in aP _L is sufficient to rule out any semantical or hidden-variable proposal which imposes this strong condition, for anytwo-or-higher dimensional Hilbert spaceP _L structure. Thus from the orthomodular lattice perspective, the peculiarly non-classical feature of quantum mechanics and the peculiarly non-Boolean feature of the quantum propositional structures is the existence of incompatible magnitudes and propositions. However, the weaker truth-functionality condition can instead be imposed upon the semantic or hidden-variable mappings on theP _L structures, although such mappings ignore the lattice meets and joins of incompatibles and preserve only the partial-Boolean algebra structural features of theP _L structures. Or alternatively, the quantum propositional structures can be taken to be partial-Boolean algebrasP _A, where bivalent mappings which preserve the operations and relations of aP _A need only be truth-functional (c). In either case, the Gleason, Kochen-Specker proofs show that any semantical or hidden variable proposal which imposes this truth-functionality (c) condition is impossible for anythree-or-higher dimensional Hilbert spaceP _A orP _L structures. But such semantical or hidden-variable proposals are possible for any two dimensional Hilbert spaceP _A orP _L structures, in spite of the presence of incompatibles in these structures, in spite of the fact that Heisenberg's Uncertainty Principle applies to the incompatible elements in these structures, and in spite of the fact that these structures are non-Boolean in the Piron sense. The present paper is a sequel of the proceedings of theSociety of Exact Philosophy annual meeting, published in our issue 9:2, pp. 187–278. — Ed. I am indebted to my supervisor, Dr. Edwin Levy, for many hours of helpful discussion on the drafts leading to this paper.     

Interpolation in 16-Valued Trilattice Logics

In a recent paper we have defined an analytic tableau calculus \({{\mathbf {\mathsf{{PL}}}}}_{\mathbf {16}}\) for a functionally complete extension of Shramko and Wansing’s logic based on the trilattice \({SIXTEEN}_3\). This calculus makes it possible to define syntactic entailment relations that capture central semantic relations of the logic—such as the relations Open image in new window , Open image in new window , and Open image in new window that each correspond to a lattice order in \({SIXTEEN}_3\); and Open image in new window , the intersection of Open image in new window and Open image in new window . It turns out that our method of characterising these semantic relations—as intersections of auxiliary relations that can be captured with the help of a single calculus—lends itself well to proving interpolation. All entailment relations just mentioned have the interpolation property, not only when they are defined with respect to a functionally complete language, but also in a range of cases where less expressive languages are considered. For example, we will show that Open image in new window , when restricted to \(\mathcal {L}_{tf}\), the language originally considered by Shramko and Wansing, enjoys interpolation. This answers a question that was recently posed by M. Takano.     

A masked priming ERP study of letter processing using single letters and false fonts

Previous event-related potential (ERP) research on letter processing has suggested that a P150 reflects lowlevel, featural processing, whereas a P260 reflects high-level, abstract letter processing. In order to investigate the specificity of these effects, ERPs were recorded in a masked priming paradigm using matching and nonmatching pairs of letters (e.g., g-g, g-j) and false fonts (e.g.,      

Equivalents for a Quasivariety to be Generated by a Single Structure

We present some equivalent conditions for a quasivariety of structures to be generated by a single structure. The first such condition, called the embedding property was found by A.I. Mal′tsev in [6]. It says that if are nontrivial, then there exists such that A and B are embeddable into C. One of our equivalent conditions states that the set of quasi-identities valid in is closed under a certain Gentzen type rule which is due to J. Łoś and R. Suszko [5]. Presented by Jacek Malinowski     

O niektórych nowych wynikach meta-matematycznych dotyczących teorii mnogości

Artykuł jest nieco zmienionym i rozszerzonym tekstem odczytu, wygłoszonego przez autora na sympozjum filozofii naukowej w Londynie w lipcu 1965. Angielski tekst odczytu ukaże się w sprawozdaniach z tego sympozjum. Allatum est die 23 Februarii 1966     

Preattentive texture segmentation: The role of line terminations,size, and filter wavelength

The texel pair represents a dilemma in texture discrimination because, despite having the same component orientations, discrimination is still possible (Julesz, 1981), showing a performance asymmetry. Other possible element properties that could influence this task are line terminations, closure, and the size of these elements. We found that line terminators are critical for the task; however, results from double-task experiments indicated that terminator-based discrimination requires the use of attention. When attention is not available for the task, “size” of the elements (with the considered slightly larger) seems to be critical for this discrimination and for the asymmetric performance. To generalize the concept of “size” to textures in general, further experiments were performed with textures of different-sized elements. Results showed, as past literature has indicated, that there is a performance asymmetry, with the larger of the elements being more visible when in the foreground. This asymmetry was additionally shown to reverse itself (i.e., the smaller element became the more visible) as the scale of the elements increased (while interelement distance remained fixed). A filter analysis was developed in order to measure the apparent size of these elements within textures (texsize), defined as the response weighted average of the filter wavelength, $\bar \lambda $ , for a group of elements. The calculation of $\bar \lambda $ was attained by introducing a nonlinearity after the second stage of filtering (or spatial averaging of filter responses). This analysis showed high correlation between the texture with the larger $\bar \lambda $ and the more visible texture. On the basis of this correlation, a wavelength-dependent noise is proposed, having more internal noise for low-spatial-frequency filters and less for high-spatial-frequency filters.     

Analityczne komponenty definicji arbitralnych

Tre: Wstp. I. Definicje arbitralne. II. Syntetyczne konsekwencje definicji arbitralnych III. Analityczne i rzeczowe komponenty definicji arbitralnych. IV. Zdania analityczne.Artyku ten w nieznacznym tylko stopniu róni si od pracy doktorskiej, któr przedstawiem w 1962 r. Jak najuprzejmiej dzikuj Prof. Dr M. Kokoszyskiej-Lutman, Prof. Dr J. Supeckiemu oraz Doc. Dr M. Przeckiemu za szereg uwag i wskazówek, z których tak wiele skorzystaem przygotowujc ostateczn redakcj pracy.     

Decomposability of the Finitely Generated Free Hoop Residuation Algebra

In this paper we prove that, for n > 1, the n-generated free algebra in any locally finite subvariety of HoRA can be written in a unique nontrivial way as Ł₂ × A′, where A′ is a directly indecomposable algebra in . More precisely, we prove that the unique nontrivial pair of factor congruences of is given by the filters and , where the element is recursively defined from the term introduced by W. H. Cornish. As an additional result we obtain a characterization of minimal irreducible filters of in terms of its coatoms. Presented by Daniele Mundici     

Expanding Quasi-MV Algebras by a Quantum Operator

We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety of such quasi-MV algebras has a subquasivariety whose members—called cartesian—can be obtained in an appropriate way out of MV algebras. After showing that cartesian . quasi-MV algebras generate ,we prove a standard completeness theorem for w.r.t. an algebra over the complex numbers. Presented by Heinrich Wansing     

Proper Semantics for Substructural Logics,from a Stalker Theoretic Point of View

We study filters in residuated structures that are associated with congruence relations (which we call -filters), and develop a semantical theory for general substructural logics based on the notion of primeness for those filters. We first generalize Stone’s sheaf representation theorem to general substructural logics and then define the primeness of -filters as being “points” (or stalkers) of the space, the spectrum, on which the representing sheaf is defined. Prime FL-filters will turn out to coincide with truth sets under various well known semantics for certain substructural logics. We also investigate which structural rules are needed to interpret each connective in terms of prime -filters in the same way as in Kripke or Routley-Meyer semantics. We may consider that the set of the structural rules that each connective needs in this sense reflects the difficulty of giving the meaning of the connective. A surprising discovery is that connectives , ⅋ of linear logic are linearly ordered in terms of the difficulty in this sense. Presented by Wojciech Buszkowski     

Prototetyka St. Lesniewskiego

Streszczenie Prototetyka St. Len'ewskiego jest uogólnieniem dwuwartociowego rachunku zda. Wystpuj w niej obok terminów tego rachunku funktory (zarówno stae jak i zmienne) tych wszystkich kategorii semantycznych, jakie mog by zdefiniowane, gdy punktem wyjcia jest kategor a zda.W pracy zreferowane s trzy systemy prototetyki. Terminem pierwotnym dwu z nich jest implikacja, terminem pierwotnym systemu trzeciego jest równowano. Systemy o terminie pierwotnym implikacji róni s. reguami wnioskowania. W jednym z nich obowizuje regua weryfikacji, w drugim regua ekstensjonalnoci. Pierwsza z tych regu jest uogólnieniem nastpujcej reguy rachunku zda, wzbogaconego o terminy 0 i 1:Wyraenie jest tez systemu, gdy tezami systemu s oba wyraenia powstae z przez podstawienie za pewn jego zmienn symboli 0 i 1.W myl reguy ekstensjonalnoci tezami systemu s prawa ekstensjonalnoci, sformuowane dla funktorów dowolnych kategorii semantycznych wac-wych prototetyce.W pracy podaj dowody równowanoci trzech systemów prototetyki i dowód ich zupenoci.Znaczna cz wyników Leniewskiego, zreferowanych w pracy, nie bya dotd opublikowana. Opracowujc te wyniki opieraem si na notatkach z wykadów Leniewskiego, spisanych przez jego uczniów. Oryginalne notatki Leniewskiego ulegy zniszczeniu w czasie powstania warszawskiego.