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A thought inspired by Friday’s Daf (page) in the Talmud, Nazir 60

A thought inspired by Friday’s Daf (page) in the Talmud, Nazir 60

The role of symbols.

This post presents a philosophical idea inspired by the text of today’s Daf. The Daf is one page in the Talmud that tens of thousands of people study each day. I explain the connection to the text in a comment below. My purpose is to show that there are underlying philosophical assumptions in the Talmud that can have great significance for anybody today trying to understand our complex reality.

What is the role of symbols in our thinking? Symbols can be letters on a page or sounds in the air. They can also be actions, such as interrupting someone or wearing formal clothes to work.

We seek to use logic to create and infer new insights. Symbolic logic, like algebra, combines multiple statements where the same symbol will appear more than once. In order to use logic, it must be possible to substitute one appearance of a symbol with another appearance of the same symbol elsewhere. The following inference, ‘Socrates is a man, all men are mortal, therefore Socrates is mortal,’ becomes hopelessly wrong if the words ‘Socrates,’ ‘man/men,’ and ‘mortal’ are not replaceable. If what I really mean is, ‘Socrates is a type-A-man, all type-B-men are mortal, therefore Socrates is mortal,’ the logic fails. The same is true for all mathematics or linguistic reasoning.

Reasoning takes multiple assertions and generates what we see as novel insights. The ability to substitute the symbol in one context for the same symbol in another context is the key to the value of our insights.

The issue at hand is that our symbols do not consistently hold the same meaning across different contexts and periods of time. For example, words such as “reason” and “greater” immense richness of different meanings. As another example, the rise of social media has caused a shift in the meaning of words such as “friend”. The cognitive tsunami that should be caused by GPT technology will also inevitably alter our understanding of words like “human behavior” and the categories we restrict it.

On the other hand, it is the richness and multiplicity of meanings that allows us to learn something new when we combine two statements. By combining our knowledge of Socrates and mortals, for example, we can gain a deeper understanding of both. Similarly, our understanding of the word “greater” can be enriched by considering its various contexts of usage. However, in doing so, we are violating the requirement of substitutability, as the meanings of the combined statements are not identical.

Without precision, reasoning fails. With precision, there is little to reason about.

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Source: Reditt