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Hace 3 días · In 1931, a twenty-five-year-old Austrian logician called Kurt Gödel published the Incompleteness Theorems, which proved two fundamental limitations in maths. First, they proved that there are mathematical truths which can’t be proven, and second, that maths itself can’t be proven to be internally consistent using its fundamental assumptions and deductive rules.
Hace 3 días · It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them.
Hace 4 días · In summary, then, Aristotle left: (1) an ontology conceived as a theory of real entities in general and of their most general aspects; this discipline is defined; (2) two quite different systems of logic: a technology of discussion and an object-linguistic formal logic; (3) a considerable overlapping of both disciplines (for example, the ...
Hace 3 días · I reconstruct a phenomenological legitimation of the demodalization, but I remain skeptical about its wider prospects. Nevertheless, the phenomenological-modal approach to negation answers the skepticism about the very possibility of debates about negation and gives valuable insight into the fundamental nature of the problem.
Hace 5 días · In the foundations of mathematics, von Neumann–Bernays–Gödel set theory ( NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel–choice set theory (ZFC). NBG introduces the notion of class, which is a collection of sets defined by a formula whose quantifiers range only over sets.
Hace 2 días · As the name suggests propositional logic is a branch of mathematical logic which studies the logical relationships between propositions (or statements, sentences, assertions) taken as a whole, and connected via logical connectives.
Hace 4 días · Definition and related disciplines. Philosophy of logic is the area of philosophy that studies the nature of logic. Like many other disciplines, logic involves various philosophical presuppositions which are addressed by the philosophy of logic. The philosophy of logic can be understood in analogy to other discipline-specific branches of philosophy: just like the philosophy of science ...
