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Vor 3 Tagen · Russell tries to support Mathematics in Logic (the school of Logicism) and paradoxically shakes the Theory of Sets. Gödel will be the one to create a crisis similar to and maybe greater than that of asymmetries in ancient Greece, by Godel’s incompleteness theorem. From now on, mathematics and their philosophy will never be the same again ...
Vor 3 Tagen · Over the last decade, however, modern deep neural networks (DNNs), which share the same fundamental design principles as their predecessors, have come to dominate artificial intelligence, exhibiting the most advanced cognitive behaviors ever demonstrated in machines. In particular, large language models (LLMs), DNNs trained to predict the next word on a large corpus of text, have proven ...
Vor 4 Tagen · This fundamental fact about scientific inquiry is well captured by an observation made by Herbert Simon, who probably thought more about problem solving than anyone before or since: “there is merit to the claim that much problem solving effort is directed at structuring problems, and only a fraction of it at solving problems once they are structured” (Simon 1973, 187).
Vor 5 Tagen · Gödel Numbering in Discrete Systems. Shawn. 12.7k. This is one of my rare threads in the Logic and Philosophy of Mathematics section. Please be aware that I am not a professional academic talking about logic; but, rather a layman trying to better understand the intricacies of logic and, in this case, Gödel numbering in discrete ordered systems.
Vor 3 Tagen · In particular, large language models (LLMs), DNNs trained to predict the next word on a large corpus of text, have proven capable of sophisticated behaviors such as writing syntactically complex sentences without grammatical errors, producing cogent chains of reasoning, and even writing original computer programs -- all behaviors thought to require compositional processing. In this chapter, we ...
Vor 4 Tagen · [a] [b] Analytic philosophy is characterized by a style of clarity of prose and rigor in arguments, making use of formal logic and mathematics, and, to a lesser degree, the natural sciences. [3] [4] [c] [d] [e] It is further characterized by an interest in language and meaning known as the linguistic turn.
Vor 5 Tagen · MATH 1500073. ChefIceMoose50. 5/22/2024. View full document. Logic: The Foundation of Rational Thought and Computational Precision Logic is the systematic study of the principles of valid reasoning and inference. It forms the backbone of mathematics, computer science, philosophy, and linguistics, enabling clear and structured thinking. This ...
