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Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.
Ludwig Wittgenstein
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Interpretation

What this quote means

Mathematics serves as a tool for understanding the world rather than as a standalone source of meaning.

In this quote, Ludwig Wittgenstein emphasizes that mathematical reasoning is not an end in itself but a means to connect and infer ideas that are grounded in the non-mathematical aspects of life. He suggests that while mathematical propositions are logical constructs, true understanding comes from applying these constructs to the complexities of human experience and thought, which cannot be encapsulated by numbers or formulas alone.

Themes

MathematicsLogicPhilosophyUnderstandingPropositionsLife

In practice

Example use cases

In a lecture on the application of mathematics in philosophy, this quote can illustrate the limitations of mathematical reasoning in understanding human experience.

More from Ludwig Wittgenstein

If we spoke a different language, we would perceive a somewhat different world.
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One cannot guess how a word functions. One has to look at its use and learn from that. But the difficulty is to remove the prejudice which stands in the way of doing this. It is not a stupid prejudice.
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It's impossible for me to say one word about all that music has meant to me in my life. How, then, can I hope to be understood?
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Nothing is so difficult as not deceiving oneself.
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My day passes between logic, whistling, going for walks, and being depressed. I wish to God that I were more intelligent and everything would finally become clear to me - or else that I needn't live much longer.
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