`I always lie' is a paradox because if it is true it must be false.
Examples of paradox
paradox
Indeed, some may feel there is too much paradox for him to be a good role model.
From the economist.com
The poignant paradox is that by losing their identity, they have transcended it.
From the washingtonpost.com
Recent, highly publicized cases of child medical neglect highlight this paradox.
From the newsweek.com
This kind of behavior, contends McCulley, is what the paradox of thrift demands.
From the time.com
In more recent times, the paradox has been described using the analogy of twins.
From the sciencedaily.com
It's a mixed compliment that hints at the paradox of the country's oil industry.
From the businessweek.com
If you don't want to talk about your glorious paradox, then why even mention it?
From the evangelicaloutpost.com
I am not sure if the paradox you mention is a Malthusian paradox or a neologism.
From the economist.com
That's another paradox of what the Tea Party Express is up to, I suggest to her.
From the guardian.co.uk
More examples
(logic) a statement that contradicts itself; "`I always lie' is a paradox because if it is true it must be false"
A paradox is a statement that, despite apparently sound reasoning from true premises, leads to a self-contradictory or a logically unacceptable conclusion. Some logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking.
Paradox is an album by John Kay and Steppenwolf, released in 1984 (see 1984 in music). It was originally released only in Canada and Australia.
Paradox is the pseudonym of Dev Pandya, a producer from the UK who has in recent years championed a new sub-genre of drum & bass known as drumfunk, which focuses on either finding obscure breakbeats or re-sampling much used drum & bass breakbeats from their original source and transforming them ...
Paradox was a Canadian band formed in the 1980's by singer/guitarist Sylvain Cossette. The band's best known lineup featured Sylvain on vocals, Francois Cossette (guitar), Denis Lavigne (drums), and Jean-Francois Houle (bass). The band broke up in 1991.
Paradox is an English indie-rock band, originating in the small village of Woodplumpton, Lancashire, England. ...
Paradox is a relational database management system currently published by Corel Corporation. It was originally released for DOS by Ansa Software, and then by Borland after it bought the company. A Windows version was released by Borland in 1992.
A self-contradictory statement, which can only be true if it is false, and vice versa. ^transl.^ usage; A counterintuitive conclusion or outcome. ^usage^ syn; A claim that two apparently contradictory ideas are true. ^transl; A person or thing having contradictory properties. ^syn. ...