Showing papers on "Class (philosophy) published in 1977"
TL;DR: The term "combined simulation" is not sufficiently well understood in the literature yet to mean one and only one specific methodology or problem class - especially since the author tends to use it in a slightly different way than most people do.
Abstract: The term "combined simulation" is not sufficiently well understood in the literature yet to mean one and only one specific methodology or problem class. One can find references where e.g., combined simulation is used as synonym for hybrid simulation. This term, therefore, requires some definition first to clarify how it is going to be used in this context - especially since the author tends to use it in a slightly different way than most people do.
27 citations
TL;DR: In this chapter, the classes of modal, coherent, and strongly coherent connectives are studied, via the corresponding classes of operators, and it is seen that "modal" and "strongly coherent" are equivalent, and that they imply "coherent" but not conversely.
Abstract: In the Kripke semantics for propositional modal logic, a frame W = (W, <) represents a set of "possible worlds" and a relation of "accessibility" between possible worlds. With respect to a fixed frame IW, a proposition is represented by a subset of W (regarded as the set of worlds in which the proposition is true), and an n-ary connective (i.e. a waybf forming a new proposition from an ordered n-tuple of given propositions) is represented by a function fW: (p(W))y -* P(W). Finally a state of affairs (i.e. a consistent specification whether or not each proposition obtains) is represented by an ultrafilter over W. {To avoid possible confusion, the reader should forget that some people prefer the term "states of affairs" for our "possible worlds".} In a broader sense, an n-ary connective is represented by an n-ary operator f = {fw 'I E Fr}, where Fr is the class of all frames and each fW (P(W))n -* P(W). A connective is modal if it corresponds to a formula of propositional modal logic. A connective C is coherent if whether C(Pi, * *, Pn) is true in a possible world depends only upon which modal combinations of P1, * * , Pn are true in that world. (A modal combination of P1, * * *, Pn is the result of applying a modal connective to P1, * * , Pn.) A connective C is strongly coherent if whether C(P1, * * , Pn) obtains in a state of affairs depends only upon which modal combinations of P1, * * *, Pn obtain in that state of affairs. In ?1 we study the classes of modal, coherent, and strongly coherent connectives, via the corresponding classes of operators. We shall characterize model-theoretically (i.e. without reference to the formulas of modal logic) these classes of operators, and we shall see that "modal" and "strongly coherent" are equivalent, and that they imply "coherent" but not conversely. A (normal modal propositional) logic L is functionally complete if every coherent operator on Fr(L), the class of all frames for L, is modal. The usual functional completeness theorems for the classical propositional calculus (every truth table is realized by a formula) and for S5 (every array of partial truth tables is realized by a formula [3, ?38.0]) may be interpreted as asserting the functional completeness, in the present sense, of CPC (i.e. K + (p <-+ Lp)) and of S5. In ?2 we shall determine which logics are functionally complete.
1 citations
01 Jan 1977
TL;DR: It would seem clear that prior to operatory classifications based on additive class inclusions in extensions and on objective equivalences of different orders in intension, there exists a mode of classification based on the relationship between actions which are functional in two ways, i.e. as the applications of schemes of actions and as the expressions of dependences.
Abstract: When children set up classifications prior to the constitution of classes based solely on similarities and differences, i.e., on a system of objective equivalences, we observe an initial stage in which there exist only ‘figural collections’2 where the following principle applies: not only are the elements of a class spatially arranged in such a way as to give the latter an overall shape (row, rectangle, etc.), but also (at least in the case of simpler forms) in such a way that one element is linked to another by reason of various ‘suitabilities’ (‘convenances’) which are unrelated to similarity. For example, a triangle is placed on a square in order to make a house and its roof, a nail with a hammer, a fir tree with a hut (instead of with another fir tree), etc. We also know that the early definitions made by children are not made on the basis of ‘kind and specific difference’ (last stage), but rather by ‘usage’ as evidenced by the use (in all languages) of the words ‘it’s for’: a mountain ‘is for climbing’, a snail ‘is for crushing’, etc. It would therefore seem clear that prior to operatory classifications based on additive class inclusions in extensions and on objective equivalences of different orders in intension, there exists a mode of classification based on the relationship between actions which are functional in two ways, i.e. as the applications of schemes of actions and as the expressions of dependences.
01 Jan 1977
TL;DR: Since languages like these can be precisely described by providing the definitions of a sentence and of direct consequence (relativized to the classes of empirical situations), and since such investigations are promising and useful for the methodology of the sciences based on experience, it seems that they should be covered equally well by epistemological discussions.
Abstract: The structure of the language in which our knowledge is expressed is more and more frequently the object of investigation of contemporary epistemological research where it is being studied from the point of view of syntax (relations between the expressions of language), semantics (relations between expressions and the objects to which these expressions refer) and pragmatics (relations between the expressions and the individuals who use them). The above studies endeavour to speak about languages which are characterized as precisely as possible by the definitions of 1) a sentence, and 2) direct consequence. In general, these languages possess the property that both of the above mentioned definitions can be formulated without reference to extralinguistic reality. They are the so-called structural languages. In the syntactic theory of such languages there is no place for, e.g., the concept of empirical thesis, which may be very useful in the methodology of the empirical sciences. On the other hand this concept can be obtained, like many others, in the syntax of empirical languages1 for which the concept of direct consequence should be characterized with extralinguistic reality in view. Since, in our opinion, languages like these can, too, be precisely described by providing the definitions of a sentence and of direct consequence (relativized to the classes of empirical situations), and since such investigations are promising and useful for the methodology of the sciences based on experience, it seems that they should be covered equally well as the structural languages by epistemological discussions. Hence, speaking of language, I shall have in mind here a language that may, equally well, be either structural or empirical. I shall only assume that it is characterized by 1) the definition of a sentence, and 2) the definition of direct consequence with regard to the classes of empirical situations (when these classes are reduced to an empty class of empirical situations, we deal with a structural language; if at least one such class is non-empty, the language is empirical). All languages characterized in this way may be considered formalized languages, since their form is precisely stated.