All the colors together make black – yes.
All the colors together make white – yes.
How can they both be true?
First we need to understand what color is.
We see a color when light of a specific range of wavelengths hits the cone receptors in the back of our eyes. We have only 3 different cone receptors: those that receive red, blue and green wavelengths. All the other colors we “see” are our brain’s interpretation of the varying wavelengths in between the 3 primary colors. For example: what we see as yellow is both the green and red cones being activated, cyan is when both green and blue cones are triggered, and magenta is when the red and blue cones are simultaneously affected.
So what is happening when we see white?
Simple, when all three of the cone types are activated at the same time, we see white. Inversely, black is when nothing activates any of the cones.
But why is it when we take all the paint colors and mix them together, we see black?
That gets us to the next thing we need to understand about light. Light waves are constantly hitting then bouncing off of surfaces, where some are absorbed into the surface itself. The color of different surfaces is determined by which wavelengths are reflected and which are absorbed. The darker a surface is, the more light is being absorbed into it. Basically, pigments create a variety of permeable surfaces, soaking up the light, so that by the time several pigment colors are added together, very little light can escape, thus we have black.
Now in the modern world of design, we rarely deal with pigment-based color. Our devices directly generate the light we work with, making for much purer and vibrant colors. This also holds true for colored light projected onto a white screen, because although it is reflected light, there is still nothing actually absorbing the light. When we see black on the monitor or screen, it is not absorbed light, it is a complete absence of light waves. Inversely, white is when all the wavelengths are projected simultaneously activating all of our eyes color receptors.
So, although all the colors together make black, they ONLY do so when the absorptive properties of the surface that the light is reflecting off of increase.
The rest of the time, all the colors together make white.