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EN
This paper deals with the problem of semantic analysis of contexts involving so-called anaphoric chain. The notion of anaphoric chain is explained by way of an example. Afterwards, a semantic analysis of sentences containing anaphora established in Transparent Intensional Logic (TIL) is examined. It is demonstrated that it is not adequate for texts including anaphoric chains. An alternative method using TIL that is capable to deal with all kinds of anaphora is proposed. Anyway, one may raise doubts as to whether both approaches are really analyses of anaphoric used expressions.
EN
In this paper we revisit Pavel Tichý’s novel distinction between one-dimensional and two-dimensional conception of inference, which he presented in his book Foundations of Frege’s Logic (1988), and later in On Inference (1999), which was prepared from his manuscript by his co-author Jindra Tichý. We shall focus our inquiry not only on the motivation behind the introduction of this non-classical concept of inference, but also on further inspection of selected Tichý’s arguments, which we see as the most compelling or simply most effective in providing support for his two-dimensional account of inference. Main attention will be given to exposing the failure of one-dimensional theory of inference in its explanation of indirect (reductio ad absurdum) proofs. Lastly, we discuss shortly the link between two-dimensional inference and deduction apparatus of Tichý’s Transparent Intensional Logic.
EN
In this paper, the authors deal with sentences containing time references like ‘five years ago’, ‘three years older’, ‘in five seconds’. It turns out that such sentences are pragmatically incomplete, because there is an elliptic reference to a calendar that makes it possible to determine the length of the time interval associated with time duration like a year, month, day, or to compute the time interval denoted by terms like ‘February 29, 2016’. Since Transparent Intensional Logic (TIL) takes into account two modal parameters, namely possible worlds of type ω and times of type τ, and this system is particularly apt for the analysis of natural language expressions, our background theory is TIL. Within this system, the authors define time intervals, calendar time durations, and last but not least a method for adding and multiplying time durations in a way that takes into account the leap days and leap seconds. As sample applications, they analyse two sentences, to wit, “A year has 365 days” and “Adam is 5 years older than Bill”.
EN
The concept of expressivity of a theory or a system (for example a system of concepts or – derivatively – of basic expressions) is surely important: a theory (system) is the more expressive the more problems it allows to be solved. We will try to formulate or at least to suggest an explication of this notion. We will, of course, assume that an appropriate explication of the notion of problem has been given.
EN
The author defends the view that the notion of concept, if used in the logical (not cognitivist) tradition, should be explicated procedurally (i.e., not set-theoretically). He argues that Tichý’s Transparent Intensional Logic is an apt tool for such an explication and derives the respective definition. Some consequences of this definition concern the notions of emptiness, simple concepts, empirical concepts and algorithmic concepts.
EN
It is shown that: (a) classicality is connected with various criteria some of which are fulfilled by TIL while some other are not; (b) some more general characteristic of classicality connects it with philosophical realism whereas (radical) anti-realism is connected with non-classical logics; (c) TIL is highly expressive due to its hyperintensionality, which makes it possible to handle procedures as objects sui generis. Thus TIL is classical in obeying principles of realism and non-classical in transcending some principles taught by textbooks of classical logic.
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