To venture to say or suggest something, often used when you're not entirely confident but think something is probably true.
'Dare' comes from Old English 'durran' (to dare), and 'say' from 'secgan.' Combined as 'dare say,' meaning 'I venture to assert,' it became a single word 'daresay' especially in British English as a way to express cautious opinion.
You'll hear this a lot in British literature and speech ('I daresay it will rain tomorrow'), and it's a wonderful way of expressing an opinion while hedging your bets—it sounds both confident and humble at the same time.
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