Frege. Jena, Forstweg To the Volunteer. Ludwig Wittgenstein 10 Frege is referring here to his essay “Der Gedanke, ein Logische Untersuchung”. show how this theory developed between the early Grundlagen der. Arithtnetik and the late essay Der Gedanke. This much is of merely exegetical interest, but it . PDF | Michael Dummett has advanced, very influentially, the view that Frege. expresses this in his most important paper,. 'Der Gedanke'.
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PDF | The founder of modern logic and grandfather of analytic philosophy was 70 years old when he published his paper 'Der Gedanke' (The Thought) in Back to Entry · Entry Contents · Entry Bibliography · Academic Tools · Friends PDF Preview · Author and Citation Info; Back to Top Complete Chronological Catalog of Frege's Work; Locations of English Gall and E. Winter, Die analytische Geometrie des Punktes und der Geraden und ihre .. [a] 'Der Gedanke. Der Gedanke kann also nicht die Be- deutung des Satzes sein, vielmehr werden wir ihn als den Sinn aufzufassen haben. Wie ist es nun aber mit der Bedeutung.
Studies at University —74 [ edit ] Frege matriculated at the University of Jena in the spring of as a citizen of the North German Confederation.
In the four semesters of his studies he attended approximately twenty courses of lectures, most of them on mathematics and physics. His most important teacher was Ernst Karl Abbe —; physicist, mathematician, and inventor. Abbe gave lectures on theory of gravity, galvanism and electrodynamics, complex analysis theory of functions of a complex variable, applications of physics, selected divisions of mechanics, and mechanics of solids.
Abbe was more than a teacher to Frege: he was a trusted friend, and, as director of the optical manufacturer Carl Zeiss AG, he was in a position to advance Frege's career. After Frege's graduation, they came into closer correspondence.
His other notable university teachers were Christian Philipp Karl Snell —86; subjects: use of infinitesimal analysis in geometry, analytical geometry of planes , analytical mechanics, optics, physical foundations of mechanics ; Hermann Karl Julius Traugott Schaeffer —; analytical geometry, applied physics, algebraic analysis, on the telegraph and other electronic machines ; and the philosopher Kuno Fischer —; Kantian and critical philosophy.
Many of the philosophical doctrines of the mature Frege have parallels in Lotze; it has been the subject of scholarly debate whether or not there was a direct influence on Frege's views arising from his attending Lotze's lectures. Work as a logician[ edit ] Main article: Begriffsschrift Though his education and early mathematical work focused primarily on geometry, Frege's work soon turned to logic.
The Begriffsschrift broke new ground, including a rigorous treatment of the ideas of functions and variables. Frege's goal was to show that mathematics grows out of logic , and in so doing, he devised techniques that took him far beyond the Aristotelian syllogistic and Stoic propositional logic that had come down to him in the logical tradition.
Title page to Begriffsschrift In effect, Frege invented axiomatic predicate logic , in large part thanks to his invention of quantified variables , which eventually became ubiquitous in mathematics and logic, and which solved the problem of multiple generality.
Previous logic had dealt with the logical constants and, or, if A frequently noted example is that Aristotle's logic is unable to represent mathematical statements like Euclid's theorem , a fundamental statement of number theory that there are an infinite number of prime numbers.
Frege's "conceptual notation", however, can represent such inferences. One of Frege's stated purposes was to isolate genuinely logical principles of inference, so that in the proper representation of mathematical proof, one would at no point appeal to "intuition".
If there was an intuitive element, it was to be isolated and represented separately as an axiom: from there on, the proof was to be purely logical and without gaps. Having exhibited this possibility, Frege's larger purpose was to defend the view that arithmetic is a branch of logic, a view known as logicism : unlike geometry, arithmetic was to be shown to have no basis in "intuition", and no need for non-logical axioms.
Already in the Begriffsschrift important preliminary theorems, for example a generalized form of law of trichotomy , were derived within what Frege understood to be pure logic.
This idea was formulated in non-symbolic terms in his The Foundations of Arithmetic Later, in his Basic Laws of Arithmetic vol. Most of these axioms were carried over from his Begriffsschrift , though not without some significant changes.
The crucial case of the law may be formulated in modern notation as follows. Thoughts may both be expressed in sentences with more content than is needed to express the Thought, or not expressed at all due to a sentence lacking certain features.
The Philosophy of Arithmetic: Frege and Husserl
Regarding the former case, Frege cites expressive and poetic words as not assisting in the expression of Thoughts; logically, such words are extraneous, whatever their function in everyday language use.
As already mentioned, Frege does not think Thoughts are external, sensible objects: truth attaches to Thoughts, but not to sensed objects, and so they cannot be the same. Frege disarms the skeptical claim that, for all we know, Ideas are all that exist. Frege levels two arguments against the claim: one, at least one independent object is needed to best explain our experiences.
To Frege, selves — conscious entities that possess Ideas — cannot be explained in terms of Ideas. He finds it is far more reasonable to posit the self as an independent object than it is to attempt an explanation of selves as specific portions of conscious content.
The second argument is pragmatic: to accept the claim that only Ideas exist is to give up on all substantive inquiry, all of which assumes the existence of external objects in order to be meaningful. This is an unacceptable outcome and thus skepticism is to be rejected. Thus, Thoughts are the bearers of truth, but do not exist as external objects nor as Ideas.
This grasping in turn leads us to action; Thoughts as such have an indirect causal impact on the world.His contributions to the philosophy of language include:. Pohle, Jena. He has already defined one and zero; they are each unique, but different from each other.
Page number reference is to the translation in Van Heijenoort.
Carnap's notes from these lectures, in German, are reproduced in Gabriel  pp. White trans. In the four semesters of his studies he attended approximately twenty courses of lectures, most of them on mathematics and physics.