By Johan van Benthem
That philosophical topics should be studied in an actual demeanour by means of logical capability used to be a pleasant discovery to make. till then, the single outlet for a philosophical curiosity identified to me was once the construction of poetry or essays. those technique of expression stay inconclusive, besides the fact that, with a bent in the direction of profuseness. The logical self-discipline offers so me highbrow spine, with no with the exception of the literary modes. A master's thesis by way of Erik Krabbe brought me to the topic of annoying good judgment. The doctoral dissertation of Paul N eedham awaked me (as such a lot of others) from my dogmatic slumbers in regards to the latter's mono poly at the logical examine of Time. ultimately, a collection of lecture notes via Frank Veltman confirmed me how classical version conception is simply as appropriate to that examine as extra unique intensional suggestions. Of the authors whose paintings encouraged me so much, i'd point out Arthur past, for his impossible to resist combination of common sense and philosophy, Krister Segerberg, for his technical starting up of a scientific conception, and Hans Kamp, for his mastery of most of these issues right now. Many colleagues have made useful reviews at the prior types of this article. i need to thank specifically my scholars Ed Brinksma, Jan van Eyck and Wilfried Meyer-Viol for his or her logical and cultural feedback. The drawings have been contributed via the flexible Bauke Mulder. eventually, Professor H intikka's type appreciation supplied the stimulus to jot down this book.
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Additional resources for The Logic of Time: A Model-Theoretic Investigation into the Varieties of Temporal Ontology and Temporal Discourse
We formalize some ofthese ideas, not only for their intrinsic interest, but also in order to see which relation they bear to the preceding ones. It will appear that there is no clash: the preceding axiomatic theories do possess models satisfying these global intuitions. Moreover, in this way, we can filter out some of the less desirable non-standard models obtained earlier on. Finally, there are some consequences for a choice of direct axioms, as will be seen below. Connectedness One simple but important idea is that no two points in time should be utterly unrelated.
It will be c;lear that Reichenbach's main concern is only tangential to the issues prominent in this book. This eminent philosopher and logician did not unite his two interests in this case. ) Maybe this is one more example ofthe unfortunate division into disjoint 'Euclidean' (logico-mathematical) and 'Aristotelean' (physical) problem traditions noted in Suppes (1973). 2. GLOBAL INTUITIONS In logical semantics it may happen that one has trouble formulating precise conditions for being a model of a certain type of statement, although one does have ideas as to which kind of model is intended.
On the contrary, the interplay between standard and non-standard models far axiomatic theories has 47 POINTS become increasingly fruitful in logic. Moreover, the categorial point ofview often suggests structural analogies between different ontologies, which may be quite informative. For instance, in Chapter IA. the categories of point structures and of period structures will be linked in this way. Strict1y speaking, it is not correct to refer to 'the category' of point structures, as different choices of morphisms yield different categories.