Electromagnetic radiation, such as light, can appear to act like waves, like particles, or both. Are these two ways of thinking about electromagnetic radiation contradictory?

Yes

Explanation:

The phenomenon is referred to as wave-particle duality. This is the concept that describes the behaviour of a wave like particles, like waves or  like both particles and waves.

These two are contradictory to each other because waves can only behave as matter (particles) or only as waves at a time. Waves can not behave as both simultaneously. Hence this concept can also be referred to as wave-particle paradox.

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