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Winston knows that Syme is guilty of thoughtcrime, and he has no confidence that he will not be found out at some point. Thus, he doesn't expect Syme to live long.
Syme and Winston have a conversation about what Syne is working on. Syme is quite excited about the prospect of the English language being shortened into an emotionally void set of word-phrases. Syme is way too excited for his own good. His passion would indicate a sense of "own life". The Party hates this.