Uploaded June 2022 | Updated September 2026, 20 hours ago

---

BCQM's eighteenth originality - Axiomata Veritatis (Axioms of the Truth): The Reflection on Hilbert's Program


比起一個遊戲玩家，我更希望自己被稱作一個音樂創作者。即使知道音樂影片的觀看數會非常少，我仍要求自己一定要做到完美，不論是音樂本身、或是影片剪輯，都要毫無瑕疵。正如同大衛‧希爾伯特對數學的嚴謹性目標，確保一切數學形式化後，保有完備性、一致性、以及確定性。然而，這樣的堅持已被庫爾特‧哥德爾證明為無法辦到，一個蘊含皮亞諾算數公理的形式系統不可能擁有完備性、也不能證明自身的一致性，同時他與保羅‧寇恩德出的結果結合後更找到了不確定命題的例子。因此，現實是不完備、不一致、更不確定的。
受到李斯特‧費倫茨所啟發，我同樣認為一切感想都可以由音樂所表達。為了提醒自己，我著手製作這項音樂計劃。起初，我將其命名為真理的形式化，在最後改為真理的公理。其內容為約長達20分鐘的鋼琴獨奏組曲，共分三樂章，曲名直接取自於希爾伯特計劃中最重要三點的反義詞：不完備性、不一致性、以及不確定性。
我雖然不是一個技術夠好的鋼琴家，在電腦科技的協助下，我仍能滿意地傳達我的音樂想法。同時我也希望未來我能有更好的技術演奏自己的作品，謝謝您的欣賞。

Compared to a gamer, I prefer to be called a music creator. Although I know that music videos gain fewer views, I still always make myself do everything perfectly, both in music itself and in video editing, and stop until they’re flawless. Just like David Hilbert’s goal in mathematics, he wanted to provide secure foundations for all mathematics, i. e., a formulation of all mathematics with completeness, consistency, and decidability. However, Kurt Friedrich Gödel proved that the goal is impossible in 1931. A consistent system of axioms can’t prove all truths, neither can it demonstrate its consistency. Together with Paul Joseph Cohen’s discovery, examples of undecidable statements were found. Hence, the reality is incomplete, inconsistent, and undecidable at the same time.
Inspired by Liszt Ferencz, I also think that music can express every thought. In order to remind myself, I started this musical project. Originally, I named it Formulation of Truth, changing it to Axiomata Veritatis (Axioms of the truth) in the end. The content is a suite of piano solo roughly 20 minutes with 3 movements, and they are named directly after the antonyms of the 3 main goals from Hilbert’s program: Incompleteness, Inconsistency, and Undecidability.
I’m not good enough at playing piano, but with the help of computer, I can still express my musical thoughts and share them with you. Meanwhile I also hope I can play the instrument with improved technique in the future and play my own piece. Thank you for watching.


Teaser:
youtu.be/QJwvprNDbdY

Other music, originalities and piano covers:
youtube.com/playlist?list=PLE0D_II109lLNuO9umF7CAO-nO5V_PlAP

Sheet music is available now!
drive.google.com/drive/u/1/folders/1NVbJzOa0BOZFvuEDiZwBFore1isqybIH


Sheet Music: Musescore
Display: Piano From Above
Recording: OBS studio
Editing: AviUtl


0:02 Incompleteness
5:30 Inconsistency
11:24 Undecidability
18:33 Finale