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The sentence:

Beethoven did outlive many people who were the same age as Berlioz.

The context:

I’m reading the book Probability Theory: the Logic of Science written by E. T. Jaynes. I was confused by the wording “logically contradictory”. I mean here. Maybe I made a mistake. I didn’t get the meaning of that sentence/counterexample in this statement:

If A implies B then a false propposition implies all propositions, and if we tried to interpret this as logical deducibility, it would follow that every false proposition is logically contradictory. Yet the proposition: ‘Beethoven outlived Berlioz’ is false but hardly logically contradictory.

By the same age as Berlioz(11 December 1803 – 8 March 1869, died at 66 years old) does the author mean 66? Or any age in one year between 1803 and 1827? Or maybe anything else? I guess what the so-called "logically contradictory" means is A => A bar(A implies the opposite of A itself)?

PS: Beethoven(1770-1827, died at 57 years old)

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    When we say A outlived B, we usually mean B died earlier (by the calendar) than A, regardless of how old each was when they died. – FumbleFingers Jul 8 '16 at 1:50
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    @FumbleFingers Then the meaning is that many people who were born at 1803(given that they were the same age as Berlioz) died at any year between 1803 and 1827. – Lerner Zhang Jul 8 '16 at 5:16
  • @lerneradams Yes. The sentence basically means, "Beethoven died later than many people who were born after him (in 1803)." – James Wirth Jul 8 '16 at 5:54
  • @lerner adams: Yes to your comment above. The sentence can be restated "Many people who were born on the same day Berlioz was born (or in the same year) died before Beethoven died". The sentence contains no information about dates or years, only relative timelines. – Tᴚoɯɐuo Jul 8 '16 at 13:01
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To "outlive" means to live or exist longer than someone or something:

  • He outlived all of his brothers.

I can't really tell what "the same age" particulary means here but my suggestion is that is means 'similarity in age' or maybe a 'stage of an age' (~45 to 65 is a middle-aged person).

It's a false conclusion to think that the statement ‘Beethoven outlived Berlioz’ is a logical contradiction rather than a false assumption.

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Outlive simply means to continue living after another has died; it does not imply anything about the age of either party.

I certainly expect that my children will outlive me

I outlived my opponent

The original sentence:

Beethoven did outlive many people who were the same age as Berlioz

...says that Beethoven died after many people who were younger than him.

Looking at the wider context, it looks as though the author is trying to clarify their language (ironic, given how confused this text becomes!). They're saying that the statement "Beethoven outlived Berlioz" is false (because Beethoven died before Belioz), but this is only known empirically (because we know the details of both mens' lives), not logically. It is not logically impossible for Beethoven to have outlived Berlioz; we can only know Beethoven did NOT outlive Berlioz from historical accounts.

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