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Last active Aug 2, 2019
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Plan for 2019 S2 seminar

S2 2019

According to the history of logic in the Encyclopaedia Britannica, logic emerged from the study of philosophical arguments, and the realisation that were general patterns by which one could distinguish valid and invalid forms of argumentation. The systematic study of logic was begun by Aristotle, who established a system of formal rules and strategy for reasoning. The use of the word strategy is intentional:

The practice of such techniques in Aristotle’s day was actually competitive, and Aristotle was especially interested in strategies that could be used to “win” such “games.” Naturally, the ability to predict the “answer” that a certain line of questioning would yield represented an important advantage in such competitions. Aristotle noticed that in some cases the answer is completely predictable—viz., when it is (in modern terminology) a logical consequence of earlier answers. Thus, he was led from the study of interrogative techniques to the study of the subject matter of logic in the narrow sense—that is, of relations of logical consequence. These relations are the subject matter of the four other books of the Organon. Aristotle nevertheless continued to conceive of logical reasoning as being conducted within an interrogative framework.

This background helps to explain why for Aristotle logical inferences are psychologically necessary. According to him, when the premises of an inference are such as to “form a single opinion,” “the soul must…affirm the conclusion.” The mind of the reasoner, in other words, cannot help but adopt the conclusion of the argument.

Talk on deep learning

Computer vision --> AlexNet NLP --> Transformer (Manning) Go, chess engines --> AlphaGo, AlphaZero

Sometimes in order to explain mathematics we describe it as the study of patterns. Fundamentally we are interested in patterns so that we can predict the future, and "win" whatever "game" we happen to be playing. In their present incarnation, in some specific games, neural networks are sufficiently capable that we must admit that they implicitly understand the patterns present in these games, and in a deep way. This is analogous to argumentation, pre-Aristotle. But this is not yet logic.

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