Transcendent arguments for God. The reason they can be undercut is that they try to explain certain features of the world that seem impossible given a physicalist (atheistic) causal story. However, one can counter with other intuitions about the world that seem impossible given a theistic account of the world.
These would include argument from desire, aesthetic beauty, religious experience. One could counter with arguments from apathy, ugliness, irreligious in the supposed religious.
The arguments below are excerpted from Peter Kreeft at
http://www.peterkreeft.com/topics-more/20_arguments-gods-existence.htm#18
Desire:
- Every natural, innate desire in us corresponds to some real object that can satisfy that desire.
- But there exists in us a desire which nothing in time, nothing on earth, no creature can satisfy.
- Therefore there must exist something more than time, earth and creatures, which can satisfy this desire.
- This something is what people call "God" and "life with God forever."
Aesthetic beauty:
1. Examine the music of Johann Sebastian Bach or painting/architecture of Da Vinci, or sculpture of Michelangelo, one will find all are universally perceived as more beautiful than their contemporaries work.
2. Beauty can only be so objectively is there is a standard of beauty that is outside of culture
3. The only possible explanation of the existence of a standard of objective beauty is found in a personal creative being who is that standard.
Religious Experience:
- Many people of different eras and of widely different cultures claim to have had an experience of the "divine."
- It is inconceivable that so many people could have been so utterly wrong about the nature and content of their own experience.
- Therefore, there exists a "divine" reality which many people of different eras and of widely different cultures have experienced.
Luckily enough the Christian God has not made the knowledge bar the standard. It is not knowledge that seems to keep people from engaging God.