Why isn't the ${\gamma}^5$ matrix not called ${\gamma}^4$?

This is not really a physical question, but it relates to notation in QED.

The ${\gamma}^5$ matrix is defined as

$${\gamma}^5=i{\gamma}^0 {\gamma}^1{\gamma}^2{\gamma}^3$$

Wouldn't it be more logical to write ${\gamma}^5$ as ${\gamma}^4$?

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