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

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?

• Sorry I am not an English native speaker and I don't know how to name it. Now I have made a rectification.
– user47471
Commented Jul 23, 2020 at 3:24
• Same for a priori Commented Jul 23, 2020 at 3:27
• But I think a priori is something natural and innate, but primitive notion is something regulated.
– user47471
Commented Jul 23, 2020 at 3:34
• That is confusing because readers cannot know if your definition is your personal one, or as an example the ones given in Wikipedia: en.m.wikipedia.org/wiki/A_priori_and_a_posteriori Commented Jul 23, 2020 at 3:42
• A priori is more typically applied to judgments and arguments, i.e. sources of knowledge, rather than to notions/concepts, the latter are more typically called innate. Primitive concepts need not be innate, they can be chosen by convention based on pragmatic considerations. Innateness itself is relative, what is not gained in the personal experience of an individual can be gained historically or by evolution, like Chomsky's innate grammar. Relationships between innate knowledge and concepts are discussed in SEP Commented Jul 23, 2020 at 5:24

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).

• Why is there a 'synthetic' before a priori?
– user47471
Commented Jul 24, 2020 at 1:32
• When discussing judgements according to Immanuel Kant, it is custom to declare whether the judgements are synthetic or analytic. However, as this distinction is not relevant for your question you can just skip it. Or read here: en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction
– user14511
Commented Jul 24, 2020 at 4:48
• But why is it synthetic? I think these statements are definitely true.
– user47471
Commented Jul 24, 2020 at 4:50
• Yes, they are true and yet synthetic. That is not contradictory. Synthetic is too complex an idea to be explained in these comments. The posted Wiki-article might help.
– user14511
Commented Jul 24, 2020 at 4:53
• That's why it reads: "[...] using a priori according to Kant [...]". All the judgements in my answer are according to Kant and not according to someone else who might be using a priori or synthetic (nowadays).
– user14511
Commented Jul 24, 2020 at 18:43