無に帰す is a literary expression meaning “to return to nothingness” or “to come to naught.” It combines 無 (nothingness) with 帰す (to return), giving it a philosophical and dramatic feeling.
In the song, it appears in 「結局どこまで行けど無に帰す」, suggesting that no matter how far people go, everything ultimately returns to nothing. Its unusual, poetic phrasing makes it a memorable expression to learn.
"ア・ポステリオリ" opens with a sneer: "笑わせないで" [don't make me laugh]. The singer has been holding it in for ages, "腹の奥底でグッと堪えてる" [biting it back deep in my gut], while watching someone who thinks they have life figured out. Over that person's head, threads are being strung everywhere, and they haven't noticed. While they are busy mocking others, "糸が絡んでる" [the threads are getting tangled]. It's a puppet image, and it is a little cruel in the best way.
The chorus is the bit that sticks: "生きる程に人は腐っていく" [the longer people live, the more they rot]. Trends fade, everything returns to nothing, and yet the narrator shrugs and calls this place "ここはパラダイス" [this is paradise] until people get bored of being human. There's a nasty little twist near the end, too: "君は言う程出来た人じゃない バレてる" [you're not as great as you claim, everyone can tell]. Then the camera turns around. Suddenly it's "瞬く度に僕は腐っていく" [every time I blink, I rot], and the last line flips the whole thing: "腐っていく中で 僕は育っていく" [while rotting, I am growing].
Word nerd corner: the title is the Latin philosophy term a posteriori, meaning knowledge you only get from experience. That fits a song whose point is that living is both what spoils you and what grows you. Also watch 気付きっこない: the ending 〜っこない is a casual way of saying "there's no way that will happen", so the line means "no way you'll notice".