I randomly followed a couple of links from LT's starting post, and I came across an article that purports to answer atheists, and it concludes with the following, and I found it to be very disappointing:
The Proper Reply
The explanation of a second method must begin with a more direct confrontation with atheism. If the existence of God cannot be deduced by cosmology, have we dodged the burden of proof and left the battlefield in the possession of our enemies? No; there is indeed a theistic answer. Superficially, it is not difficult to understand; but, unfortunately, a full appreciation of its force requires some philosophic expertise. A knowledge of geometry is of great help, but it is seldom taught in the public high schools. One cannot realistically expect Christians to have read and to have understood Spinoza; and Protestant churches usually anathematize plain, ordinary Aristotelian logic.
In geometry there are axioms and theorems. One of the early theorems is, "An exterior angle of a triangle is greater than either opposite interior angle." A later one is the famous Pythagorean theorem: the sum of the squares of the other two sides of a right triangle equals the square of its hypotenuse. How theological all this sounds! These two theorems and all others are deduced logically from a certain set of axioms. But the axioms are never deduced. They are assumed without proof.
There is a definite reason why not everything can be deduced. If one tried to prove the axioms of geometry, one must refer back to prior propositions. If these too must be deduced, there must be previous propositions, and so on back ad infinitum . From which it follows: If everything must be demonstrated, nothing can be demonstrated, for there would be no starting point. If you cannot start, then you surely cannot finish.
Every system of theology or philosophy must have a starting point. Logical Positivists started with the unproved assumption that a sentence can have no meaning unless it can be tested by sensation. To speak without referring to something that can be touched, seen, smelled, and especially measured, is to speak nonsense. But they never deduce this principle. It is their non-demonstrable axiom. Worse, it is self-contradictory, for it has not been seen, smelled, or measured; therefore it is self-condemned as nonsense.
If the axioms of other secularists are not nonsense, they are nonetheless axioms. Every system must start somewhere, and it cannot have started before it starts. A naturalist might amend the Logical Positivist’s principle and make it say that all knowledge is derived from sensation. This is not nonsense, but it is still an empirically unverifiable axiom. If it is not self-contradictory, it is at least without empirical justification. Other arguments against empiricism need not be given here: The point is that no system can deduce its axioms.
The inference is this: No one can consistently object to Christianity’s being based on a non-demonstrable axiom. If the secularists exercise their privilege of basing their theorems on axioms, then so can Christians. If the former refuse to accept our axioms, then they can have no logical objection to our rejecting theirs. Accordingly, we reject the very basis of atheism, Logical Positivism, and, in general, empiricism. Our axiom shall be, God has spoken. More completely, God has spoken in the Bible. More precisely, what the Bible says, God has spoken.
But my answer to all this is, no mathemetician states that 'Triangle' exists. It is simply a description used for objects in the real world. Triangle is no more a real object than Consensus or Blue or Minority.
