ISO is linear scale and perception is log scale. Doubling the ISO (while keeping the shutter speed the same) increases the exposure by only one stop, which won’t seem twice as bright.
No, it's twice as bright physically (in the sense that the lux value doubles). For example, doubling the shutter speed increases the exposure by one stop. Similarly, increasing the diameter of the aperture by a factor of √2 (thus doubling the area of the aperture and letting twice as much light in) increases the exposure by one stop.
