Tradition holds that...

[Tofu]

Hello Alan, Mister Micawber, Beeesneees, Mordant, Esl_Expert and other native English speakers,

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http://www.oxfordadvancedlearnersdictionary.com/dictionary/hold
hold
(formal) to consider that something is true
[hold that…] I still hold that the government's economic policies are mistaken.
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http://news.yahoo.com/s/ap/eu_france_da_vinci
Tradition holds that the "Mona Lisa" is a painting of Lisa Gherardini, wife of Florentine merchant Francesco del Giocondo, and that da Vinci started painting it in 1503.
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Does holds mean to consider that something is true?

[Beeesneees]

Try substituting 'upholds the idea that'
If you uphold something you support and maintain it, therefore you would consider it true.
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Cheers m' dears!

[Tofu]

Thank you, B.