ALBERT

Notes: Abstract A semantical proof of Craig's interpolation theorem for the intuitionistic predicate logic and some intermediate prepositional logics will be given. Our proof is an extension of Henkin's method developed in [4]. It will clarify the relation between the interpolation theorem and Robinson's consistency theorem for these logics and will enable us to give a uniform way of proving the interpolation theorem for them.

Notes: Abstract Important positive as well as negative results on interpolation property in fragments of the intuitionistic propositional logic (INT) were obtained by J. I. Zucker in [6]. He proved that the interpolation theorem holds in purely implicational fragment of INT. He also gave an example of a fragment of INT for which interpolation fails. This fragment is determined by the constant falsum (⊥), well known connectives: implication (→) and conjunction (∧), and by a ternary connective δ defined as follows: δ (p, q, r)= df (p∧q)∨(ℸp∧r). Extending this result of J. I. Zucker, G. R. Renardel de Lavalette proved in [5] that there are continuously many fragments of INT without the interpolation property. This paper is meant to continue the research mentioned above. To be more precise, its aim is to answer questions concerning interpolation and amalgamation properties in varieties of equivalential algebras, particularly in the variety determined by the purely equivalential fragment of INT.

Notes: Abstract The logic of the weak law of excluded middleKC p is obtained by adding the formula ℸA ∨ ℸ ℸA as an axiom scheme to Heyting's intuitionistic logicH p . A cut-free sequent calculus for this logic is given. As the consequences of the cut-elimination theorem, we get the decidability of the propositional part of this calculus, its separability, equality of the negationless fragments ofKC p andH p , interpolation theorems and so on. From the proof-theoretical point of view, the formulation presented in this paper makes clearer the relations betweenKC p ,H p , and the classical logic. In the end, an interpretation of classical propositional logic in the propositional part ofKC p is given.

Notes: Abstract Intermediate prepositional logics we consider here describe the setI(Ω) of regular informational types introduced by Yu. T. Medvedev [7]. He showed thatI(Ω) is a Heyting algebra. This algebra gives rise to the “logic of infinite problems” from [13] denoted here asLM 1. Some other definitions of negation inI(Ω) lead to logicsLM n (n ⩽ ω). We study inclusions between these and other systems, proveLM n to be non-finitely axiomatizable (n ⩽ ω) and recursively axiomatizable (n 〈 ω). We also show that formulas in one variable do not separateLM ∞ from Heyting's logicH, andLM n (n 〈 ω) from Scott's logic (H+S).

Notes: Abstract I distinguish between sentences like (1) Last Thursday we drove from Wellington to Waikanae and (2) Last Thursday my copy of Aspects of the Theory of Syntax remained on my bookshelf. Sentence (2) has the subinterval property. If it is true at an interval t it is true at every subinterval of t. (1) lacks this property. (1) reports an event. (2) reports a state. Events do not have the subinterval property but states do have it, and so do objects. If something is a linguist at an interval t then that person is a linguist at all subintervals of t. I argue that ‘exists’ applies to things which have the subdinterval property, and ‘occurs’ applies to things which lack it.

Notes: Abstract The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.

Notes: Abstract The main part of the proof of Kripke's completeness theorem for intuitionistic logic is Henkin's construction. We introduce a new Kripke-type semantics with semilattice structures for intuitionistic logic. The completeness theorem for this semantics can he proved without Henkin's construction.

Notes: Abstract For intermediate logics, there is obtained in the paper an algebraic equivalent of the disjunction propertyDP. It is proved that the logic of finite binary trees is not maximal among intermediate logics withDP. Introduced is a logicND, which has the only maximal extension withDP, namely, the logicML of finite problems.

Notes: Abstract Coming fromI andCl, i.e. from intuitionistic and classical propositional calculi with the substitution rule postulated, and using the sign ο to add a new connective there have been considered here: Grzegorozyk's logicGrz, the proof logicG and the proof-intuitionistic logicI Δ set up correspondingly by the calculi For any calculusи we denote byяи the set of all formulae of the calculusи and byℒи the lattice of all logics that are the extensions of the logic of the calculusи, i.e. sets ofяи formulae containing the axioms ofи and closed with respect to its rules of inference. In the logiclɛℒG the sign □ is decoded as follows: □A = (A & ΔA). The result of placing □ in the formulaA before each of its subformula is denoted byTrA. The maps are defined (in the definitions of x and λ the decoding of □ is meant), by virtue of which the diagram is constructed In this diagram the mapsσ, x andλ are isomorphisms, thereforex −1 = λ; and the maps △ andμ are the semilattice epimorphisms that are not commutative with lattice operation +. Besides, the given diagram is commutative, and the next equalities take place:σ −1 =μ −1 λ△ and σ = △−1 xμ. The latter implies in particular that any superintuitionistic logic is a superintuitionistic fragment of some proof logic extension.

Notes: abstract Section 1 contains a Kripke-style completeness theorem for arbitrary intermediate consequences. In Section 2 we apply weak Kripke semantics to splittings in order to obtain generalized axiomatization criteria of the Jankov-type. Section 3 presents new and short proofs of recent results on implicationless intermediate consequences. In Section 4 we prove that these consequences admit no deduction theorem. In Section 5 all maximal logics in the 3 rd counterslice are determined. On these results we reported at the 1980 meeting on Mathematical Logic at Oberwolfach. This paper concerns propositional logic only.

Notes: Abstract The aim of this paper is to provide a decision procedure for Dummett's logic LC, such that with any given formula will be associated either a proof in a sequent calculus equivalent to LC or a finite linear Kripke countermodel.

Notes: Abstract It is well known that the manner in which a definitely descriptive term contributes to the meaning of a sentence depends on the place the term occupies in the sentence. A distinction is accordingly drawn between ordinary contexts and contexts variously termed ‘non-referential’, ‘intensional’, ‘oblique’, or ‘opaque’. The aim of the present article is to offer a general account of the phenomenon, based on transparent intensional logic. It turns out that on this approach there is no need to say (as Frege does) that descriptive terms are referentially ambiguous or to deny (as Russell does) that descriptive terms represent self-contained units of meaning. There is also no need to tolerate (as Montague does) exceptions to the Principle of Functionality. The notion of an ordinary (i.e., ‘non-intensional’) context is explicated exclusively in terms of logical structure and it is argued that two aspects of ordinariness (termed ‘hospitality’ and ‘exposure’) must be distinguished.

Notes: Abstract In the paper [2] the following theorem is shown: Theorem (Th. 3,5, [2]), If α=0 or δ=∞ or α⩾δ, then a closure space X is an absolute extensor for the category of 〈α, δ〉 -closure spaces iff a contraction of X is the closure space of all 〈α, δ〉-filters in an 〈α, δ〉-semidistributive lattice. In the case when α=ω and δ=∞, this theorem becomes Scott's theorem: Theorem ([7]). A topological space X is an absolute extensor for the category of all topological spaces iff a contraction of X is a topological space of “Scott's open sets” in a continuous lattice. On the other hand, when α=0 and δ=ω, this theorem becomes Jankowski's theorem: Theorem ([4]). A closure space X is an absolute extensor for the category of all closure spaces satisfying the compactness theorem iff a contraction of X is a closure space of all filters in a complete Heyting lattice. But for separate cases of α and δ, the Theorem 3.5 from [2] is proved using essentialy different methods. In this paper it is shown that this theorem can be proved using, for retraction, one uniform formula. Namely it is proved that if α= 0 or δ= ∞ or α ⩾ δ and $$F_{\alpha ,\delta } \left( L \right) \subseteq B_{\alpha ,\delta }^\mathfrak{n} $$ and if L is an 〈α, δ〉-semidistributive lattice, then the function $$r:{\text{ }}B_{\alpha ,\delta }^\mathfrak{n} \to F_{\alpha ,\delta } \left( L \right)$$ such that for x ε ℘ ( $$\mathfrak{n}$$ ): (*) $$r\left( x \right) = inf_L \left\{ {l \in L|\left( {\forall A \subseteq L} \right)x \in C\left( A \right) \Rightarrow l \in C\left( A \right)} \right\}$$ defines retraction, where C is a proper closure operator for $$B_{\alpha ,\delta }^\mathfrak{n} $$ . It is also proved that the formula (*) defines retraction for all 〈α, δ〉, whenever L is an 〈α, δ〉 -pseudodistributive lattice. Moreover it is proved that when α=ω and δ=∞, the formula (*) defines identical retraction to the formula given in [7], and when α = 0 and δ=ω, the formula (*) defines identical retraction to the formula given in [4].

Notes: Abstract The notion of local deduction theorem (which generalizes on the known instances of indeterminate deduction theorems, e.g. for the infinitely-valued Łukasiewicz logic C ∞) is defined. It is then shown that a given finitary non-pathological logic C admits the local deduction theorem iff the class Matr(C) of all matrices validating C has the C-filter extension property (Theorem II.1).

Notes: Abstract The first part of the paper deals with some subclasses of B-algebras and their applications to the semantics of SCI B , the Boolean strengthening of the sentential calculus with identity (SCI). In the second part a generalization of the McKinsey-Tarski construction of well-connected topological Boolean, algebras to the class of B-algebras is given.

Notes: Abstract We give an idea of uniform approach to the problem of characterization of absolute extensors for categories of topological spaces [21], closure spaces [15], Boolean algebras [22], and distributive lattices [4]. In this characterization we use the notion of retract of the closure space of filters in the lattice of all subsets.

Notes: Abstract D. Scott in his paper [5] on the mathematical models for the Church-Curry λ-calculus proved the following theorem. A topological space X. is an absolute extensor for the category of all topological spaces iff a contraction of X. is a topological space of “Scott's open sets” in a continuous lattice. In this paper we prove a generalization of this theorem for the category of 〈α, δ〉-closure spaces. The main theorem says that, for some cardinal numbers α, δ, absolute extensors for the category of 〈α, δ〉-closure spaces are exactly 〈α, δ〉-closure spaces of 〈α, δ〉-filters in 〈α, δ〉-semidistributive lattices (Theorem 3.5). If α = ω and δ = ∞ we obtain Scott's Theorem (Corollary 2.1). If α = 0 and δ = ω we obtain a characterization of closure spaces of filters in a complete Heyting lattice (Corollary 3.4). If α = 0 and δ = ∞ we obtain a characterization of closure space of all principial filters in a completely distributive complete lattice (Corollary 3.3).

Notes: Abstract Given an intermediate prepositional logic L, denote by L −d its disjuctionless fragment. We introduce an infinite sequence {J n}n⩾1 of propositional formulas, and prove: (1)For any L: L −d =I −d (I=intuitionistic logic) if and only if J n∉ L for every n ⩾ 1. Since it turns out that L∩{J n} n⩾1 = Ø for any L having the disjunction property, we obtain as a corollary that L −d = I −d for every L with d.p. (cf. open problem 7.19 of [5]). Algebraic semantic is used in the proof of the “if” part of (1). In the last section of the paper we provide a characterization in Kripke's semantic for the logics J n =I+ +J n (n ⩾ 1).

Notes: Abstract Let S denote the variety of Sugihara algebras. We prove that the lattice Λ (K) of subquasivarieties of a given quasivariety K $$ \subseteq $$ S is finite if and only if K is generated by a finite set of finite algebras. This settles a conjecture by Tokarz [6]. We also show that the lattice Λ (S) is not modular.

Notes: Abstract An evaluation method, similar to the two-valued one for the classical logic, is introduced to give a decision procedure for some of intermediate logics. The logics treated here are obtained from some logics by adding the axiom ℸav ℸℸa.

Notes: Abstract LetSKP be the intermediate prepositional logic obtained by adding toI (intuitionistic p.l.) the axiom schemes:S = ((ℸ ℸα→α)→α∨ ℸα)→ ℸα∨ ℸℸα (Scott), andKP = (ℸα→β∨γ)→(ℸα→β)∨(ℸα→γ) (Kreisel-Putnam). Using Kripke's semantics, we prove: 1) SKP has the finite model property; 2) SKP has the disjunction property. In the last section of the paper we give some results about Scott's logic S = I+S.

Notes: Abstract In some recent papers, the authors and Peter Gärdenfors have defined and studied two different kinds of formal operation, conceived as possible representations of the intuitive process of contracting a theory to eliminate a proposition. These are partial meet contraction (including as limiting cases full meet contraction and maxichoice contraction) and safe contraction. It is known, via the representation theorem for the former, that every safe contraction operation over a theory is a partial meet contraction over that theory. The purpose of the present paper is to study the relationship more finely, by seeking an explicit map between the component orderings involved in each of the two kinds of contraction. It is shown that at least in the finite case a suitable map exists, with the consequence that the relational, transitively relational, and antisymmetrically relational partial meet contraction functions form identifiable subclasses of the safe contraction functions, over any theory finite modulo logical equivalence. In the process of constructing the map, as the composition of four simple transformations, mediating notions of bottom and top contraction are introduced. The study of the infinite case remains open.

Notes: Abstract In our previous paper [5], we have studied Kripke-type semantics for propositional logics without the contraction rule. In this paper, we will extend our argument to predicate logics without the structure rules. Similarly to the propositional case, we can not carry out Henkin's construction in the predicate case. Besides, there exists a difficulty that the rules of inference (→∀) and (∃→) are not always valid in our semantics. So, we have to introduce a notion of normal models.

Notes: Abstract Universality of generalized Alexandroff's cube $$B_{\alpha ,\delta }^\mathfrak{n} $$ plays essential role in theory of absolute retracts for the category of ťα, δ〉-closure spaces. Alexandroff's cube. $$B_{\alpha ,\delta }^\mathfrak{n} $$ is an ťα, δ〉-closure space generated by the family of all complete filters. in a lattice of all subsets of a set of power $$\mathfrak{n}$$ . Condition P(α, δ, $$\mathfrak{n}$$ ) says that $$B_{\alpha ,\delta }^\mathfrak{n} $$ is a closure space of all 〈α, δ〉-filters in the lattice 〈π( $$\mathfrak{n}$$ ), $$ \subseteq $$ 〉. Assuming that P (α, δ, $$\mathfrak{n}$$ ) holds, in the paper [2], there are given sufficient conditions saying when an 〈α, δ〉-closure space is an absolute retract for the category of 〈α, δ〉-closure spaces (see Theorems 2.1 and 3.4 in [2]). It seems that, under assumption that P (α, δ, $$\mathfrak{n}$$ ) holds, it will be possible to givean uniform characterization of absolute retracts for the category of 〈α, δ 〉-closure-spaces. Except Lemma 3.1 from [1], there is no information when the condition P (α, δ, $$\mathfrak{n}$$ ) holds or when it does not hold. The main result of this paper says, that there are examples of cardinal numbers, α, δ, $$\mathfrak{n}$$ such that P (α, δ, $$\mathfrak{n}$$ ) is not satisfied. Namely it is proved, using elementary properties of Lebesgue measure on the real line, that the condition P (ω, ω 1, 2 ω ) is not satisfied. Moreover it is shown that fulfillment of the condition is essential assumption in, Theorems 2.1 and 3.4 from [1] i.e. it cannot be eliminated.

Notes: Abstract We say that an n-argument predicate P ⊂ Ω n is finite, if P is a finite set. Note that the set of individuals Ω is infinite! Finite predicates are useful in data bases and in finite mathematics. The logic DBL proposed here operates on finite predicates only. We construct an imbedding for DBL in a special modal logic MPL. We prove that if a finite predicate is expressible in the classical logic, it is also expressible in DBL. Quantifiers are not necessary in DBL. Some simple algebraic properties of DBL are indicated.

Notes: Abstract Beth models of analysis are used in model theoretic proofs of the disjunction and (numerical) existence property. By glueing strings of models one obtains a model that combines the properties of the given models. The method asks for a common generalization of Kripke and Beth models. The proof is carried out in intuitionistic analysis plus Markov's Principle. The main new feature is the external use of intuitionistic principles to prove their own preservation under glueing.

Notes: Abstract This paper introduces conditional logic, that is, a variant of free logic where the existence condition of a function is defined by a formula of the formal language. Syntax and semantics are developed. A completeness theorem is given.

Notes: Abstract In this paper, we shall confine ourselves to the study of sentential constants in the system R of relevant implication. In dealing with the behaviour of the sentential constants in R, we shall think of R itself as presented in three stages, depending on the level of truth-functional involvement.

Notes: Abstract There exist important deductive systems, such as the non-normal modal logics, that are not proper subjects of classical algebraic logic in the sense that their metatheory cannot be reduced to the equational metatheory of any particular class of algebras. Nevertheless, most of these systems are amenable to the methods of universal algebra when applied to the matrix models of the system. In the present paper we consider a wide class of deductive systems of this kind called protoalgebraic logics. These include almost all (non-pathological) systems of prepositional logic that have occurred in the literature. The relationship between the metatheory of a protoalgebraic logic and its matrix models is studied. The following results are obtained for any finite matrix model U of a filter-distributive protoalgebraic logic Λ: (I) The extension Λ U of Λ is finitely axiomatized (provided Λ has only finitely many inference rules); (II) Λ U has only finitely many extensions.

Notes: Summary In this report on the present state of the discussion about the interpretation of quantum mechanics an attempt is made to provide an idea of the philosophical relevance of the foundations of physics. A simplified model of the measuring process is given which shows the difficulties in the interpretation of quantum mechanics. It is argued against Bohr's solution (also in a version of H. Putnam). Two examples show possible philosophical consequences of quantum mechanics: The variety of quantum logics challenges the foundations of logic, the paradox of Einstein, Podolsky and Rosen (with Bell's inequality) may be interpreted along the lines of holism. Against alleged refutations of realism by means of quantum mechanics, a realist standpoint is maintained. A proper interpretation of quantum mechanics from an epistemological point of view seems still to be lacking. In my childhood the legend was current, that only twelve men in the World understood Einstein's theory. Nowadays, relativity is quite tame; but I shall argue presently thatnobody yet understands the quantum theory. Howard Stein

Notes: Summary This paper examines the three central theses of the Copenhagen interpretation of quantum mechanics. (1) Quantum mechanics must make use of concepts of classical physics; (2) descriptions which in classical physis are mutually exclusive are complementary descriptions of the same objects in quantum mechanics; (3) the uncertainty relations are natural laws which determine the limits of the application of classical concepts to micro-physical objects. Usually, these central theses of the Copenhagen interpretation are interpreted in a realistic-ontological manner. This paper criticizes this position, and, by means of a comparative investigation of the function of models in classical physics and quantum mechanics, proposes a model-theoretic interpretation. This interpretation lays special stress on the fictional status of models in quantum mechanics.

Notes: Zusammenfassung Asarja Polikarov ist die führende Gestalt in der Wissenschaftsmethodologie Bulgariens und einer der bedeutendsten Vertreter dieses Faches innerhalb des marxistischen Denkens. Der vorliegende Artikel ist der Analyse seiner Leitideen gewidmet: Dem Charakter des Verhältnisses zwischen Wissenschaft und Methodologie, der Konzeption des Multimethodologismus, der Untersuchung der Wertigkeit methodologischer Systeme, der Proliferation physikalischer Theorien usw. Das Ziel der Analyse besteht darin, die Stellung der Ansichten Polikarovs in Beziehung auf die weltweiten Tendenzen gegenwärtiger Wissenschaftsmethodologie aufzuweisen.

Notes: Summary The well-knownempiristical apories of the law of nature prevent until this day an adequate philosophical interpretation ofempirical science. Clarification can only be expected through animmanent refutation of the empiristical point of view. In this sense it is proved in this paper thatHume's argumentation, paradigmatic for modern empirism, is not just one-sided, but simplyinconsistent: Anyone who claimes experience to be the basis of all knowledge (as the empirist does), and, due to this, denies that the lawlike character of nature can be substantiated,has, in fact, always presupposed the lawfullness of nature, i. e. has assumed theontology of a nature lawful in itself. If this lawfullness is, more closely, understood asdependency on conditions, then the functional character of the laws of nature is involved with the consequence thatverification is not only to be understood as a mere repetition of instances of the law but as a verification of theconditional texture defined in it. Furthermore does the functionality of the law of nature also include a statement on itsinvariance (against certain transformations). This throws a new light on theproblem of induction. In this kontext it cannot be surprising that the notorious neglect of the functional aspect in the context of modern empirism has led to fundamental problems with the concept of the law of nature.

Notes: Zusammenfassung Der Streit darüber, ob es objektive Wahrheitskriterien gibt, wird oft mit der Frage vermengt, ob Wissenschaft immer fortschreite. Vor allem Popper in “Objective Knowledge” unterstellt in starkem Maße einen allgemeinen Trend der Wissenschaft zum Fortschritt. In diesem Beitrag wird gezeigt, daß Wissen verloren gehen kann: 1. Weil es nicht aufgezeichnet wird; 2. weil die Dokumente, in denen es niedergelegt wurde, verloren gehen; 3. weil das Wissen um die Sprache der Dokumente, in denen es niedergelegt wurde, verloren gegangen ist, 4. weil die spätere Wissenschaftlergemeinschaft die Dokumente nicht genügend beachtet, in denen es niedergelegt wurde. Der Verlust nichtaufgezeichneten Wissens ist äußerst üblich. Der Verlust veröffentlichter Dokumente war besonders vor der Erfindung der Drucktechnik häufig und hat besonders in manchen Zweigen der Geisteswissenschaften einen Rückschritt bedeutet, weil entweder Dokumente, die das Objekt dieser Wissenschaften ausmachen (z. B. in der Literargeschichte), oder Aufzeichnungen historischer Ereignisse verloren gingen. Der Verlust veröffentlichter Dokumente nach der Erfindung der Drucktechnik war etwas weniger bedeutend, aber er kam dennoch vor. Der Verlust unveröffentlichter Dokumente geschah häufig, und zwar sowohl vor wie nach der Erfindung der Drucktechnik. Ob in unentzifferten Dokumenten definitiv Wissensverlust vorliegt, ist einigermaßen zweifelhaft. Einige unentzifferte Sprachen mögen eines Tages entziffert werden, aber einige unentzifferte Sprachen mögen auch für immer unentziffert bleiben. Der Verlust von Wissen wegen unzureichender Aufmerksamkeit gegenüber dem Werk eines früheren Wissenschaftlers kann behoben werden, wenn man seine Behauptungen nochmals untersucht. Wissensverlust kommt hauptsächlich in den Geisteswissenschaften vor. In der Mathematik und einigen Naturwissenschaften gibt es fast nur Zunahme an Wissen wegen der Wiederholbarkeit der Experimente.

Notes: Zusammenfassung Nach vielen gegenwärtigen Wissenschaftstheoretikern ist die Wissenschaftstheorie des Logischen Empirismus, wie sie in den Schriften von Carnap, Russell, Reichenbach und Hempel vertreten wird, durch die neue Wissenschaftstheorie wesentlich verbessert worden, wie sie von Hanson, Polanyi, Toulmin und Kuhn entwickelt worden ist. Aber keiner der letzteren Gegner des Logischen Empirismus hat im Detail die Erkenntnistheorie herausgearbeitet, welche der neuen Wissenschaftstheorie zugrundeliegt. Kürzlich jedoch hat Harold I. Brown, inPerception, Theory and Commitment · The New Philosophy of Science (University of Chicago, 1979), eine klare Formulierung dieser neuen, consensualen Erkenntnistheorie vorgelegt. In dem vorliegenden Artikel entwickele und bewerte ich die Ansichten von Brown und Kuhn als Repräsentanten der neuen Erkenntnistheorie. Alles in allem begründe ich, daß die neue Erkenntnistheorie bestenfalls eine äußerst unvollständige Alternative zur logisch-empiristischen Erkenntnistheorie liefert.

Notes: Summary By means of an ecological and system theoretic example it is argued, that the methodological principle of repeatable effects is only partially valid. In 1970 a conjecture of system's properties was published which was refuted later, but further research was initiated in different fields, just because it referred to a non-repeatable „false“ result. The heuristic content of a concept seemed to be more important than a successful replication of an experiment. The case study exhibits the restricted validity of general methodological rules.

Notes: Summary The paper exposes the principal procedures of assessing methodological theories. The first one is based on a consensus about the aims of science, the second uses epistemological criteria, and the third checks the adequacy of methodological requirements against the history of science. This third procedure (Lakatos' rational reconstruction) is singled out for a more detailed treatment. It is argued that rational reconstruction constitutes a separate level of historiography (distinct from the interpretation of a scientist's thinking and the study of reception of ideas) and concerns historical explanation. The subject of a rational reconstruction is the methodological explanation ofall basic value judgments, whereas all additional factors (such as an individual scientist's choice between competing theories or his motives for this choice) are not determined by methodological rules. It is further specified in which way rationally reconstructed history should correspond to the actual course of historical events, i. e. to which extent rational reconstruction is free to interpret history according to methodological categories. In the last paragraph the connection between scientific progress and the growth of knowledge is discussed.

Notes: Summary A new reply to the old question as to meaning and foundations of the Lorentz transformations is given by passing over to non-linear equations. Thus, it is possible to show that the theory of special relativity can be based upon the Galilei transformations, i. e. on the classical assumptions concerning space and time, if terms of the fourth order are neglected. The new theory will probably give rise to a revision of relativistic mechanics.

Notes: Zusammenfassung Durch Analyse einiger zentraler Begriffe der Lebenswelt, wie z. B. Perspektivität, Intentionalität und Reflexion, wird versucht zu zeigen, daß und wie philosophisch fundierende Motive in der Lebenswelt verankert sind. Hierdurch wird wenigstens ein Teil der Grundlage enthüllt, auf der die Bedingung des Transzendierens der Lebenswelt bei der philosophischen Suche nach Einsicht und Wahrheit beruht. — Der Aufsatz versucht ebenfalls zu zeigen, daß Phänomenologie und transzendentale Pragmatik nicht unvereinbare Positionen sind. Dies hat allerdings zur Folge, daß die transzendentale Pragmatik eine Rechtfertigung durch eine Analyse ihrer lebenswichtigen Vorbedingungen zu benötigen scheint.

Notes: Zusammenfassung Negative gegenseitige Befruchtung mag als seltsamer Titel erscheinen. Gegenseitige Befruchtung scheint per definitionem etwas Positives zu sein. Aber diese Untersuchung will die Aufmerksamkeit auf die Tatsache richten, daß in einer großen Anzahl von Fällen die gegenseitige Befruchtung einige negative Effekte auslöst; einige von ihnen mögen sogar katastrophal sein. Dieser Artikel kann die Aufmerksamkeit nur auf die negativen Auswirkungen und die Notwendigkeit lenken, die Bedingungen, welche den positiven oder negativen Ausgang oder die Unwirksamkeit einer bestimmten gegenseitigen Befruchtung determinieren, ausführlicher zu untersuchen; um die Randbedingungen auf beiden Seiten zu formulieren: Das Befruchtende und das Befruchtete.

Notes: Summary This paper is about 1. cognitive science's claim to obtain an empirically theory of human (natural) intelligence by experiments with intelligent machines; 2. the question, whether simulation yields/is explanation (S:E), i.e. whether the theory explaining the behaviour of a thing A, appropriately abstracted, as well explains the behaviour of a thing B, different in type from A, when A's and B's behaviours are indistinguishable; 3. the question, whether the Aristotelian ontic distinction between the natural and the artificial was in fact extinguished by Descartes' materialistic intensional ontology; this question is denied by evidence of the existence of different theories of artificial and natural magnetism in current physics; 4. and about the comparison of the current theories of magnetism, of artificial or electromagnetism and of natural or ferromagnetism with the result that there is no uniform theory explaining all kinds of magnetism to be gained out of Maxwell's theory. Thus by counterexample is demonstrated that cognitive science's claim to obtain a theory of natural intelligence by the S:E-strategy is to be refused. Descartes' premise of the ontic indifference of the size of physical magnitudes is introduced as basis of the S:E-claim and its refutation as cause of the partial continuation of the ontic distinction between natural and artificial things in physics.

Notes: Summary This paper is an attempt to establish a general perspective on approaching the philosophy of philology historically. Part I examines the problem of relating history to philosophy of philology, with a view to stressing the importance of historical intuitions about the discipline. It is asserted that such intuitions do not exist for the whole range of philological activities but only for a certain kind. Part II gives a brief survey on the beginnings of philology in the Hellenistic Age in order to make plausible a distinction between two types of philological research: working within a ‘grammatical’ framework on the one hand, and working within a ‘critical’ framework on the other. Part III includes a list of some strong historical intuitions about progressive developments in philology of the ‘grammatical’ kind, that could function as touchstones for appraising philosophical models. In the sequel, attention is drawn to the most important types of viewing progress in science. None of them is regarded as the philosophy of philology in question, but they all appear more in tune with our historical intuitions than the prevailing relativism.

Notes: Summary The author investigates which methods of naming objects are possible in the language of physics on the basis of the real physical conditions and to which extend objects thereby can be identified. It is shown that in the language of classical physics naming by designation is always possible. But this implies only the temporal identity of objects, not the “trans — world” — identity, which is important for modalities. In the language of quantum physics naming by designation is no longer applicable to individuals but only to classes of equivalent objects. And for these classes temporal identity as well as the “trans — world” — identity can be produced, which means that an adequate semantics can be specified for the concept of possibility necessary in this language.

Notes: Summary Idealized explanations are the one subtype of incomplete explanations which is most frequently used in the empirical sciences and at the same time least analyzed in philosphy of sicence. It is argued that idealized explanations, while having the same logical structure as adequate explanations, differ from these in the mode of validity of the argument. Whereas an adequate explanation shows why the occurrence of some event had to be expected, an idealized explanation argues that a certain event would occur if certain conditions were fulfilled. Idealized explanations are heuristic devices which, in the long run, ought to be transformed into adequate explanations.

Notes: Summary Ever since the so-called linguistic revolution in philosophy, the problem of universals has become the question of whether or not abstract/general terms refer. Nominalism gives a negative answer to that question. But there is, let us say, a Continental side to nominalism which this paper sets out to explore. It examines thesocial consequences of a nominalist approach to questions of knowledge. In particular it looks in detail at 17th century science and Merton's scientific ethos and describes the effects of nominalism as a social norm of research in both fields. According to this interpretation nominalism links up cognitive and social factors. As an intermediary stage the paper examines Nietzsche's analysis of the social function of abstract terms and his view of science. Lastly, the paper indicates how a methodical nominalism can make a significant contribution towards solving the problem of relativism.

Notes: Summary While the logical reconstruction of empirical theories is, in principle, no longer a matter of dispute, the possibility and, furthermore, the procedure of constructingab initio such theories are hardly debated upon, although this might be conductive to the advancement, above all, of sciences of a pre-paradigmatic status. Eight steps are here proposed for the constructive development of an explanatory empirical theory in a strictly scientific sense, the development starting with a construction of the theory's set of partial potential models Mpp and ending up in a characterization of its range of intended applications I. The set of partial potential models is gained by way of genetic reduction of present-day practical, i. e. pre-theoretical, notions, which denote observable facts to be explained, to some possible notion of an elementary historical practice. This elementary practical notion, which must be conceived as a general notion of a formerly given elementary social practice, has afterwards to be developed into some general notion for all the phenomena to be presently explained, by way of reconstructing the historical emergence of the present field of research. The elementary practical notion also forms the basis for the generation of theexplaining so-called t-theoretical terms of the theory. Their development, however, presupposes a ‘political’ decision of the scientist to work in favour of the perfection of certain practically relevant capacities, which decision also determines the domain of discourse for the set of partial potential models of the theory and links its explaining terms to the terms denoting the facts to be explained. A set Io of successful applications of the as yet not completed theory and respective special laws, making up the success of such applications, render possible the full axiomatization of the theory as well as the characterization of the range of its intended applications.

Notes: Summary The famous thesis of the underdetermination of our theories about the world through the available observational data is the basis of Quine's skepsis which forces him to commit himself to the theses of the inscrutability of reference and the indetermination of translation. On the basis of an examination of Quine's distinction between observational and theoretical sentences, I intend to show the impossibility of translating observational sentences without their being affected by the indeterminacy of translation. They too, cannot be translated without the aid of analytical hypotheses only by equating them with observational reports of the language into which they are to be translated. The consequence of this is that the basis of this assumption, the empirical equivalence of logically incompatible systems of the world, loses its point.

Notes: Summary In logic books ordinary language examples are often thought to be easier to understand, as it is presupposed or suggested, that their logical structure is obvious. This suggestion is not only incorrect; moreover, as this paper shows (by means of E. v. Savigny's book ‘Grundkurs im logischen Schließen’), the alleged simplification in fact entails additional problems: The notion of ‘logical structure’ remains vague, and confusion between the logical features of statements and the grammatical properties of ordinary language sentences is invoked; some arbitrariness and circles in the presentation are also inevitable. It would be more helpful to clearly state the conventional character of logical systems as well as to stress the importance of semantical analysis in order to find out the logical structure of statements.

Notes: Zusammenfassung Begriffsanalyse und empirische Forschung auf dem Gebiet der künstlichen Intelligenz zeigen, daß momentan derart kontroverse Ansätze entwickelt werden, daß gemeinschaftliche Momente in Perspektiven und angewandten Methodologien nur schwer auszumachen sind.

Notes: Abstract In this paper a logical interpretation of semantic nets and graph grammars is proposed for modelling natural language understanding and creating language understanding computer systems. An example of parsing a Finnish question by graph grammars and inferring the answer to it by a semantic net representation is provided.

Notes: Abstract This essay is intended to be a systematic exposition and critique of Daniel Dennett's general views. It is divided into three main sections. In section 1 we raise the question of the nature of a plausible scientific psychology, and suggest that the question of whether folk psychology will serve as an adequate scientific psychology is of special relevance in a discussion of Dennett. We then characterize folk psychology briefly. We suggest that Dennett's views have undergone at least one major change, and proceed to discuss both his earlier and his later views. In section 2 we suggest that Dennett is correctly perceived as an instrumentalist in his earlier works. We think that Dennett later abandons this position because of general worries about instrumentalism and, more importantly, because Dennett became convinced that an instrumentalist conception of folk psychology will not enable us to vindicate the notions of personhood, moral agency, and responsibility. This left Dennett with a dilemma. On the one hand, he does not think that beliefs, etc., will turn out to be genuine scientific posits. On the other hand, he thinks that moral agency would be impossible if we could not treat beliefs, etc. as causally efficacious in some suitable sense. In section 3 we discuss Dennett's resolution of this dilemma. The key to his current view, we suggest, is the illata-abstracta distinction. Dennett holds that both illata and abstracta are real and have causal powers, even though only illata are genuine scientific posits. He suggests that beliefs etc. are abstracta, and are the subject matter of what he calls ‘intentional system theory’. The subject matter of another theory, what Dennett calls ‘subpersonal cognitive psychology’, are illata, which are subpersonal intentional states. The important point is that this distinction lets Dennett have it both ways: (i) Since beliefs are mere abstracta, we need not commit ourselves to the thesis that beliefs will turn out to be posits of an adequate scientific psychology. (ii) Since beliefs have causal power, we are assured of moral and rational agency. We shall argue that Dennett's current view is untenable. If we are right in our arguments, then Dennett's program to produce a scientifically plausible psychology, one that will turn out to vindicate folk psychology (in some suitable sense), is a failure. It fails in the following important ways: (i) What Dennett sketches — intentional system theory cum subpersonal cognitive psychology — is not a plausible scientific psychology. (ii) As a consequence, Dennett also fails to provide a satisfactory foundation for moral and rational agency.

Notes: Abstract In this paper I argue against the view, defended by some philosophers, that it is part of the meaning of “mental” that being mental is incompatible with being physical. I call this outlook metalinguistic dualism (MLD for short), and I distinguish it from metaphysical theories of the mind-body relation such as Cartesian dualism. I argue that MLD is mistaken, but I don't try to defend the contrary view that mentalistic terms can be definitionally reduced to nonmental ones. After criticizing arguments by certain philosophers which purport to establish MLD, I formulate a criterion for a phenomenon's being mental. I then show that this criterion is neutral between monistic and dualistic theories of the mind-body relation. Since if MLD were true it should be impossible to construct such a criterion, I conclude that it is false (i.e., if it is intended as a descriptive thesis about our language). The significance of my paper is that if I am right then I remove one important type of objection to aposteriori, noneliminative forms of the identity theory of mind, namely that such theories ought to be rejected merely on the basis of semantical considerations about the word “mental”. Beyond that, I believe that my criterion of mental phenomena correctly captures our intuitions about the nature of the distinction between mental and nonmental phenomena.

Notes: Abstract Certain metaphysical and epistemological presuppositions are shown to play a role in the defense of Davidson's claims that an empirically constructed theory of truth provides an adequate theory of meaning for any natural language. Dadivson puts forward demonstrative arguments in favor of these presuppositions in ‘On the Very Idea of a Conceptual Scheme’, ‘Thought and Talk’, and ‘The Method of Truth in Metaphysics’. These arguments are examined and found to include controversial and dubitable assumptions as premises. It is then suggested that both these controversial assumptions and Davidson's metaphysical and epistemological presuppositions can be partially defended, however, by dialectical, interpretive, and historical arguments that elucidate the nature of persons.

Notes: Abstract In a recent article, Grover Maxwell presents a case for a kind of mind-brain identity theory which he claims precludes materialism. His case is based on some views about meaning which I find plausible. However, I will argue that, by adopting certain assumptions about the nature of sensory experience, and extending some of Maxwell's views about meaning in a plausible way, the issue of a materialistic identity theory is reopened. Ultimately, I will agree that such a theory is not true, but more is needed to show this than Maxwell gives us. But the question of materialism is not thereby closed, because it has become axiomatic these days that materialism does not require an identity theory. So I will go on to consider if all forms of materialism have been ruled out by Maxwell's theory, as extended by me. I will end with a tentative affirmative answer but also with a proposal which, if it can be worked out, would reverse the decision.

Notes: Abstract Philosophy as a separate discipline is a rather new phenomenon. This presents problems for our understanding of what constitutes the history of philosophy. Past writers often approached their concerns from a multi-disciplinary perspective; thus to understand them we have to do more than answer a contemporary set of issues. To that end, I suggest we attend to Locke's advice on how to read a text. Following this advice may permit us to avoid several puzzles which result from misreading a text.

Notes: Abstract While Curley argues that we need to know the history of philosophy so as not to avoid important alternatives to contemporary proposals, I argue that philosophy is an essentially historical enterprise. Unlike science, philosophy cannot forget its history. Not to know the history of philosophy is not to understand why the questions we seek to answer are worth answering or asking.

Notes: Abstract Premise: our representational system has had a relatively invariant core throughout human history (cf. Sellars's “manifest image”). Major theses: (i) When philosophical argument establishes the existence of an entity, that entity is a representing, not a represented. (ii) Most of the documents in the history of philosophy are on a par (as dialogical resources) with current philosophical literature for establishing or controverting such existence claims. (iii) The use of mathematics (initially the mathematized neo-Platonism of classical mechanics) allowed modern physical science to break with the perennial system of representation; in consequence, a portion of the representings of modern physical scientists do not belong to the historically invariant core. This limits the dialogical resources of physical science and the applicability of arguments from perennial philosophy to science. It also explains the relative irrelevance of pre-17th century science to contemporary physical scientists in contrast to the relevance of pre-17th century philosophy to contemporary philosophers. It also supports thesis (iv), that logic (broadly conceived) in central to all serious philosophical enterprises, since logic is the central tool for exhibiting and criticizing the rationale(s) of our representational system(s). Support for these theses will be found in the paper.

Notes: Abstract In this comment on John Yolton's ‘Is There a History of Philosophy?’ (Yolton, 1985) I review his account of the development during the 17th to 19th centuries of a common sense of the range of philosophical problems and of the canon of philosophical works. I suggest that his account may be read in light of Rorty's four genres of historiography (Rorty, 1984). I criticize his view of the place of the history of philosophy in philosophy as too timid, though correct as far as it goes. I then suggest, but do not attempt to establish, a bolder thesis. Finally, I raise some doubts about the adequacy of Yolton's reading of Descartes and Berkeley set out in two of his ‘Puzzlements.’ The ‘Puzzlements’ themselves are supposed to illustrate typical misreading of major figures in the history of philosophy.

Notes: Abstract Serious work in history of philosophy requires doing something very difficult: conducting a hypothetical dialogue with dead philosophers. Is it worth devoting to it the time and energy required to do it well? Yes. Quite apart from the intrinsic interest of understanding the past, making progress toward solving philosophical problems requires a good grasp of the range of possible solutions to those problems and of the arguments which motivate alternative positions, a grasp we can only have if we understand well philosophy's past. Philosophers who concentrate too much on the present are apt to assume too simple a view of alternative theories and of important philosophical arguments. Ryle and Austin offer instructive examples of how it is possible to go wrong by ignoring or misrepresenting historical figures.

Notes: Abstract In recent years philosophers of science have turned away from positivist programs for explicating scientific rationality through detailed accounts of scientific procedure and turned toward large-scale accounts of scientific change. One important motivation for this was better fit with the history of science. Paying particular attention to the large-scale theories of Lakatos and Laudan I argue that the history of science is no better accommodated by the new large-scale theories than it was by the earlier positivist philosophies of science; both are, in their different ways, parochial to our conception of rationality. I further argue that the goal of scientific methodology is not explaining the past but promoting good scientific practice, and on this the large-scale methodologies have no obvious a priori advantages over the positivist methodologies they have tried to replace.

Notes: Abstract Some philosophers of science suggest that philosophical assumptions must influence historical scholarship, because history (like science) has no neutral data and because the treatment of any particular historical episode is going to be influenced to some degree by one's prior philosophical conceptions of what is important in science. However, if the history of science must be laden with philosophical assumptions, then how can the history of science be evidence for the philosophy of science? Would not an inductivist history of science confirm an inductivist philosophy of science and a conventionalist history of science confirm a conventionalist philosophy of science? I attempt to resolve this problem; essentially, I deny the claim that the history of science must be influenced by one's conception of what is important in science — one's general philosophy of science. To accomplish the task I look at a specific historical episode, together with its history, and draw some metamethodological conclusions from it. The specific historical episode I examine is Descartes' critique of Galileo's scientific methodology.

Notes: Abstract Inattention to the historical antecedents of current philosophical views may impoverish our arguments in defense of those views. A case in point, examined here, concerns the difference that can be made for current strategies designed to defend religious belief by carefully reconsidering the position of historical sceptics.

Notes: Abstract Intuitionistic meta-methodologies, which abound in recent philosophy of science, take the criterion of success for theories of scientific rationality to be whether those theories adequately explicate our intuitive judgments of rationality in exemplary cases. Garber's (1985) critique of Laudan's (1977) intuitionistic meta-methodology, correct as far as it goes, does not go far enough. Indeed, Garber himself advocates a form of intuitionistic meta-methodology; he merely denies any special role for historical (as opposed to contemporary or imaginary) test cases. What all such positions lack is a base from which to inform, criticize, or restructure our core methodological intuitions. To acquiesce in this is to deny that exemplary cases can serve the sort of warranting role required for intuitionism. This point is reinforced by a series of reasons for denying the warranting role of pre-analytic judgments of rationality. These reasons point the way toward an improved approach to meta-methodology.

Notes: Abstract Professor Penelhum has argued that there is a common error about the history of skepticism and that the exposure of this error would significantly improve our understanding of a current confusion in the philosophy of religion with regard to the issue of the rationality of religious beliefs. Penelhum considers certain contemporary philosophers of religion such as Plantinga skeptics because he reads Plantinga (for example) as arguing that religious beliefs are properly groundless in virtue of the fact that none of our beliefs have any ultimate grounds, and Penelhum argues that this sort of defense of religious belief is both limited and dangerous for religion. I argue that on the interpretation of ancient skepticism which Penelhum gives ancient skepticism is just what it has often been claimed to be: either practically untenable or incoherent or both. I show that in any case the confusion in philosophy of religion which Penelhum wants to sort out with the help of ancient skepticism is not one of which its alleged proponents are guilty. The views of Plantinga and others who take his line are more complex and powerful than Penelhum's presentation makes them seem; these views do not constitute an acceptance of skepticism but a denial of a certain sort of foundationalism. Contrary to Penelhum, then, I argue that ancient skepticism does not serve as a significant corrective for certain trends in contemporary philosophy of religion.

Notes: Abstract Proponents of causal decision theories argue that classical Bayesian decision theory (BDT) gives the wrong advice in certain types of cases, of which the clearest and commonest are the medical Newcomb problems. I defend BDT, invoking a familiar principle of statistical inference to show that in such cases a free agent cannot take the contemplated action to be probabilistically relevant to its causes (so that BDT gives the right answer). I argue that my defence does better than those of Ellery Eells and Richard Jeffrey; and that it applies, where necessary, to other types of Newcomb problem.

Notes: Abstract During the past decades several philosophers of science and social scientists have been interested in the problems of causation. Recently attention has been given to probabilistic causation in dichotomous causal systems. The paper uses the basic features of probabilistic causation to argue that the causal modeling approaches developed by such researchers as Blalock (1964) and Duncan (1975) can provide, when an additional assumption is added, adequate qualitative measures of one variableś causal influence upon another. Finally, some of the difficulties and issues involved in developing adequate quantitative measures are discussed, and it is concluded that the causal modeling measures cannot provide adequate quantitative measures.