What is the relationship between the primitive notion and a priori?

Question

The primitive notion is the origin of definition to avoid circularity since definition must be defined by other terminologies which involve new definitions. So in maths we have set, point, space and so on as primitive notion. It is like something beyond our words, can hardly be learnt from experience.
A priori is also something beyond experience. I have an intuition that there is a sutble relationship between them. If the answer is yes, then what is it?

Mr. White · Answer

There is no noteworthy connection between the two concepts. Consider the following four judgements involving primitive and non-primitive notions according to Euclidean geometry and using a priori according to Kant. The judgements cover all possible combinations:

primitive notion in a-priori judgement
non-primitive notion in a-priori judgement
primitive notion in a-posteriori judgement
non-primitive notion in a-posteriori judgement

"The angular sum in a triangle is 180°" involves the non-primitive notion of triangle and is (synthetic) a priori.
"A straight line can be drawn from any point to any point" involves the primitive notion of point and is (synthetic) a priori.
"The very triangle I have just drawn has a bigger area than the one I drew yesterday" involves the non-primitive notion of triangle and is a posteriori (and thus synthetic).
"The straight line I drew yesterday at 10am is longer than the straight line I drew today at 10am" involves the primitive notion of straight line and is a posteriori (and thus synthetic).

What is the relationship between the primitive notion and a priori?

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