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Note on Frege's Begriffsschrift.
In dieser Arbeit wird Freges Urteilsbegriff untersucht. Es gehört zu Freges Verdiensten, die Logik von den traditionellen Urteilsformen befreit zu haben: Verneinung, Bedingtheit und Allgemeinheit machen nicht unterschiedliche Formen des Urteilens aus, sondern bestimmen den Inhalt von Urteilen. Durch diese Verschiebung von der Urteilsform zum Urteilsinhalt wird der Urteilsbegriff nicht obsolet. Urteilen ist für Frege allemal eine „logische Urtätigkeit“, und die strikte Trennung zwischen dem blossen Fassen eines Gedankens (Denken) und dem Anerkennen seiner Wahrheit (Urteilen) zieht sich durch sein gesamtes Werk hindurch. In dieser Arbeit wird dargelegt, wie diese Unterscheidung zu Missverständnissen führt, wenn das Urteilen nicht als eine Art des Denkens verstanden wird. Zu diesem Zweck werden in einem ersten Schritt die Funktion des Urteilsstrichs in Freges Logik und das Urteilen im Kontext von logischen Schlüssen untersucht. In einem zweiten Schritt wird danach gefragt, ob dieser Urteilsbegriff auch unabhängig von Freges Logizismus für spontane Urteile wie Wahrnehmungsurteile oder Urteile, die Behauptungen zugrunde liegen, annehmbar ist. Mit Moores Paradox wird schliesslich dargelegt, inwiefern Urteile und Behauptungen auf die Wahrheit zielen. Am Ende wird das Problem der Einheit des Urteils aufgegriffen und gezeigt, dass Freges Begriffslehre insofern zu einer Lösung dieses Problems beiträgt, als Gedanken unterschiedlich zerfällt werden können. The thesis investigates Frege’s notion of judgment. One of Frege’s important contributions to modern logic is the abandonment of traditional forms of judgment, since according to Frege negation, conditional, and quantification have to be expressed at the level of the content of a judgment. Yet, this move does not jettison the notion of judgment—in fact, Frege thinks that judgment is a “logically primitive activity”. Throughout his whole work he distinguishes between merely grasping a thought (thinking) and acknowledging a thought as true (judging). I shall argue that this distinction leads to confusions if judging is not considered as a way of thinking. In particular, I shall examine the function of the judgment-stroke in Frege’s logical system, arguing that judgments for Frege are essentially embedded in chains of inference. The context of Frege’s logicism not only makes it plausible to require the premises of an inference to be true, it also explains why Frege almost never considers the possibility of false judgments. However, in the remainder of the thesis I shall try to make sense of judgments beyond logicism; i.e. spontaneous judgments as they occur in assertion and perception. Moore’s paradox exemplifies the way in which judgments as well as assertions aim at truth. The final chapter addresses the problem of the unity of judgments. It is argued that Frege’s logical doctrine of the decomposition of a sentence allows for a resolution of this problem.
This chapter discusses the concept of Lewis Carroll's logic. Lewis Carroll is one of those writers on logic obscured by contradictory influences, balanced between the old logic and the new trends. He is a mathematical teacher, the author of children's tales, and photographer. He is also a very prolific letter-writer and puzzle-maker, and regularly wrote pamphlets and letters to periodicals on matters as various as vaccination, teaching sciences at the university, child actors, and vivisection. Like the majority of his contemporary British colleagues, Carroll's work quickly became out-dated. His only logical contributions, which one still meet(s) with in modern textbooks, are his logic diagrams and Mind problems. Carroll's logical work shows also that he is acquainted with the logical players of his time. Reading Lewis Carroll reveals conflicting influences from both traditional and modern logicians. It also shows some interesting inventions, which deserve more attention from logicians and historians of logic.
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