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This article studies some of the relevant and historically influential conceptions of the notions of ›judgement‹ and ›proposition‹ and discusses the relationship of these notions in these conceptions. In some detail the conceptions of Aristotle, Brentano and Twardowski, Frege, Martin-Löf and of ε-theory are presented. A comparison of these conceptions shows fundamental differences which, in a way, illuminate the differences found in the architectures and formal appearances of logics.
The article studies intentionality of conceptions and presents an abstract model of conception. Intentionality of conceptions is analysed in two settings, the notion of a mental phenomenon or act, in the sense of Brentano and Twardowski, and the notion of a mental state, in the sense of Searle. To determine characteristics which separate conceptions from other mental states, the relation between conceptions (German: Auffassungen) and presentations (German: Vorstellungen) is analysed. The following is found: conceptions have intentionality, but they differ from presentations and do not fully fit the characteristics of mental phenomena. They can, on the other hand, clearly be identified as undirected intentional mental states with the distinguished role that any intentional mental state either is a conception or rests on a conception. From the study of their ontological status, and from the reading of sets as presentations and of set theories as theories of conceptions, further insight into the requirements on their modelling is provided. The model then is a conceptual metamodel the main features of which reflect the findings on conceptions as intentional mental states. It is intended to generally apply to the modelling of intentional relations and of situations with characteristics of perspectivity and of subject and context dependency.
Eine grundlegende Funktion von Bildern ist das Zeigen. Bilder zeigen sich selbst und zeigen etwas anderes. Vor einem Bild stellt sich die Frage des Sehens. Das Sehen stellt ein Bild in eine epistemischen Umgebung, in der es dem Betrachter etwas zeigt. Diese Bedingungen des Bildseins werden an Kasimir Malewitschs Schwarzes Quadrat auf wei ss em Grund und an Velasquez’ Portrait Papst Innozenz X. verdeutlicht. Anders als bei Bildern ist es eine grundlegende Funktion von Modellen etwas zu transportieren. Modelle sind Träger eines Cargo. Durch die Auffassung eines Gegenstands als Modell steht dieser Gegenstand in einer modell-typischen epistemischen Umgebung. Das Bildsein eines als Modell aufgefassten Gegenstands überlagert dessen Modellsein und tritt nicht selten in dessen Dienste. Dieses natürliche Verhältnis von Bild und Modell lässt sich an einer Zeichnung Leonhard Eulers zum Königsberger Brückenproblem und an Leonardo da Vincis Zeichnung des Vitruv-Manns darstellen.
Models are ubiquitous. They are found since the beginning of human culture, in great varieties of appearance and use. A model is always at the same time a model ›of something‹ and a model ›for something‹. Its function is to ›carry‹ some ›cargo‹ from its ›matrix‹ to its ›applicate‹. Since every object can be a model but none is a model by necessity, the question of what a model is leads to considerations on how to explain things which are being conceived of and depend on subjects and situations. Model-being can therefore not be explained through some relationship of similarity or as a form of abstraction, but only through a model which imposes a structure on the context, in which a model fulfills its function. Based on such a model of model-being, models can be questioned and thus be the subject of a general model theory.