I'm getting interested in mathematics because as a philosopher I am upset with the amazingly poor standards of rigor in my field. I am looking to mathematics for guidance. I would like to formalize philosophy and turn it into a deductive science. I have a deep interest in logic so I decided to study mathematical arguments and figure out what makes them true. Much to my surprise I have found mathematical arguments to be much more informal than I thought they would be. It seems that the rock-bottom foundations of mathematics still have not been made secure. What I'm interested in doing is proving mathematical theorems entirely in a new logical language that I've invented without resorting to notation. Essentially, I'm working on the old Russellian problem of showing that math reduces to logic. I have sort of proven Euclid's first theorem with just words alone but my logical language is still in a state of flux and I keep making adjustments to it. Plus, I have not proven it to my satisfaction. Let's now look at the Euclidean definitions for geometry as translated by Richard Fitzpatrick which amazingly has the original Greek side by side and given that I have a good knowledge of Greek I can sort of work out the original. A point is that of which there is no part. Σημεῖόν ἐστιν, οὗ μέρος οὐθέν. Has any geometer defined part? And a line is a length without breadth. Γραμμὴ δὲ μῆκος ἀπλατές. Has any geometer defined length or breadth? And the extremities of a line are points. Γραμμῆς δὲ πέρατα σημεῖα Has any geometer defined extremity? You get the idea of what I'm driving at. My theory is that if we understand the meaning of these words then we can make deductions to prove Euclid's theorems without even saying an image of what he's referring to.