How many strings does a standard violin have?

How to get close to this number

Reason from the bow. A bowed instrument can only sound one or two strings at a time because the bridge is curved, so extra strings add range rather than polyphony. Four is the fewest that covers a useful range while keeping the neck narrow enough to finger accurately.

The tuning in fifths is the design decision that matters. Fifths spread the range wide with few strings — four strings in fifths cover more pitch than six in fourths — at the cost of requiring wider finger stretches. A guitar tunes in fourths for chord shapes; a violin tunes in fifths for range.

The family point in the explanation generalises it: viola, cello and double bass all use four strings, and the first three are tuned in fifths. One design scaled across four sizes covers the entire orchestral string range, which is why a player can move between them and why the string section of the orchestra sounds like one instrument in four registers.