incendiarism (n.)

c. 1400, "person who sets malicious fires," from Latin incendiarius "an incendiary," literally "causing a fire" (see incendiary (adj.)). Meaning "person who enflames political passions" is from 1630s.

word-forming element making nouns implying a practice, system, doctrine, etc., from French -isme or directly from Latin -isma, -ismus (source also of Italian, Spanish -ismo, Dutch, German -ismus), from Greek -ismos, noun ending signifying the practice or teaching of a thing, from the stem of verbs in -izein, a verb-forming element denoting the doing of the noun or adjective to which it is attached. For distinction of use, see -ity. The related Greek suffix -isma(t)- affects some forms.

form of insanity marked by a mania for destroying things by fire, 1840, from pyro- "fire" + mania "madness, frenzy." Used in German in the 1830s.

The propensity which leads an insane person to accomplish his purpose by burning, has been considered to merit particular notice, and to constitute a variety of monomania. Dr. Marc, of France, has published a memoir on the subject; he gives the name of pyromania to it, and considers that, like other insane propensities, it may be the result of instinct, or it may be the result of delusion—reasoning upon erroneous principles. [Alexander Morrison, M.D., "The Physiognomy of Mental Diseases," London, 1840]

An older word for it was incendiarism.