人生とは、他の予定を立てることに忙しくしている時に起こる現象のことだ。

English Translation

Life is what happens to you while you’re busy making other plans.

What is the purpose of the と in とは? why is it not simply a は?

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I think it makes the following sentence a definition of life. Maybe it is short for と言うのは?

I think you could omit the と without changing the meaning too much.

とは is a specific grammatic construction that precedes a definition, whereas は is just a topic marker. It is used after a noun to elaborate on the meaning or characteristics of the noun, and it is often used in patterns like とは…ものだ or とは…ことだ. Another common ending is ということだ / 意味だ. It’s used mainly in written language, as Nということだ would be more common in spoken Japanese.

This can be seen in sentences like:

蓮華とは蓮の花のことだ。
A ‘renge’ is a lotus flower.

パソコンとは、個人で使える小型のコンピューターのことだ。
A personal computer (pasokon) is a small-sized computer for individual use.

This might be of some help:

Your example sentence fits into the definition category, but とは can also be used to show a quotation or express surprise:

A:森山さん、会社退職するそうですよ。
B:退職するとは、結婚するということですか。
A: I’ve heard Moriyama’s leaving the company.
B: Does that mean she’s getting married?

As you can see, it’s very similar to the first use, but it places emphasis on elaborating upon a statement, or seeking more information, often accompanied with an emotional response, like surprise or disdain:

一人で5種目も優勝とはまったく驚いた。
It is absolutely amazing that you won five different events on your own.

タクシーの中に忘れた現金が戻ってくるとは思いもよらないことでした。
I never expected that the cash I had left in the taxi would be returned to me.

全員そろって授業をサボるとはあきれた学生たちだ。
What an appalling group of students, all of them skipping class together.

Finally, it can be replaced with なんて in colloquial speech, and in informal situations the とは can stand on its own to express an emotional reaction, as the rest of the sentence can be inferred from context:

あの人がこんな嘘をつくとは。
(What a surprise that) that person would tell such a lie.

I don’t know your Japanese level, but hopefully this isn’t too much information at once. I hope this has been helpful to you, this is my first time responding on this forum so please let me know if there are any issues with formatting/clarity, and I’ll be sure to rectify them.

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As a native Japanese speaker, I’m very impressed with @Sirithar ‘s comprehensive explanations with example sentences. I can guarantee that all of them are correct and natural.

Let me give you guys two follow-on tips on the difference between とは and は.

  1. とは as a particle for definitions sounds more academic, scientific (i.e. fact-based), or philosophical. We don’t usually say とは in this context in a daily conversation. But you will frequently find とは in the introductory paragraphs of Wikipedia articles and other dictionaries/encyclopedias.

  2. If you replace とは with は in the context of definition, the altered sentence has a different connotation. Particle は usually highlights the gap between two things. Therefore, 人生は instead of 人生とは in this lesson sentence implies that nothing but 人生 fits the description.

By the way, the original Japanese sentence sounds very unnatural, especially due to the bad collocation of 人生 and 現象. 現象 means “phenomenons”, and is used in natural environmental changes (raining, eruption of volcano etc.), social behavioral patterns (urbanization, hoarding under the COVID pandemic etc.), or technological bugs/errors. 人生 (one’s life) is not a phenomenon caused and ceased by uncontrollable external factors. So, you cannot say 人生とは…現象だ (life is a phenomenon.)

To be honest, I don’t fully understand the English sentence either. If it means that “some unpredictable life events often happen to you when you are busy making other plans”, I would translate it into Japanese:

何か予定を立てている時こそ、往々にして予測不能なことが人生に降りかかるものだ。

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