Intuitionism
From Tractatus
Intuitionism is a Philosophy of Mathematics, which I happen to find attractive.
Anyone who believes in Mathematics, either implicitly or explicity must also carry the baggage, whether implicitly or explicitly of particular beliefs about Truth. Note that I capitalize Truth, so that the reader may discern that I am not speaking about some mere attribute like existence, but about something which transcends reality.
I was introduced to the branch of Mathematical Philosophy known as Intuitionism in Church, when speeaking with Dr. Daniel Davenport. At that time, he was using Intuitionistic logics, specifically Heyting Algebras, to aid in document analysis.
The basic principle of Intuitionism is that the basis of Belief is intuition. In order for an argument to be believable, it must be intuitive, that is it must be 'obviously true.' For example, we all have an intuitive understanding of the aritmatic of whole numbers. It is inconceivable that anyone would deny arithmatic precisely because it is intuitive... immediate to the mind.
Intuitionism is a Philosophy of Mathematics first expounded by L.E.J. Brouwer, best known for his extensive contributions to Topology