"S knows that-p a priori" can be defined in a number of ways, having nothing to do with "instinct," whatever that is.

Possibly (but not "only"), if instincts are considered as (or as involving) innate knowledge. Ethologists sometimes talk like that. "What is a priori for the individual is a posteriori for the species" is a quotation often associated with Konrad Lorenz, Herbert Spencer, and Ernst Haeckel.

https://www.rutherfordjournal.org/article010104.html

To answer the question “Is priori knowledge only instincts? Why?” it is evidently necessary before to answer the question “what is knowledge?” at all; and what is “instincts”?”

Midstream philosophy and sciences fundamentally cannot answer any of the questions above, since in the mainstream all really fundamental phenomena/notions, first of all in this case “Matter”, “Consciousness”, “Space”, “Time”, “Energy”, “Information”, are fundamentally completely transcendent/uncertain/irrational; and so in every case when the mainstream addresses to any really fundamental problem, including in this case, then result completely inevitably is transcendent/irrational, i.e. by no means scientifically grounded something.

The questions above can be, and essentially are, really scientifically answered only in framework of the Shevchenko-Tokarevsky’s really philosophical 2007 “The Information as Absolute” conception, recent version of the basic paper see

https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed

- where it is rigorously proven that there exist nothing else than some informational patterns/systems of the patterns that are elements of the absolutely fundamental and absolutely infinite “Information” Set.

So everything what exists, including the system Matter and every material structures/systems, and fundamentally non-material systems “Consciousnesses” are made absolutely for sure from one stuff “Information”, the utmost general definition of “Information” is

“Information is something that is constructed in accordance with the set/system of absolutely fundamental Rules, Possibilities, Quantities, etc. – the set/system “Logos” in the conception”

Examples of “Logos” set elements are, say, Space”, “Time”, “Energy”, “Logical Rules”, etc.

- and so if some patterns/systems compose some system, that happens only in some space; and every system is something like a computer, where the elements are “hardware”, which is logically governed by “soft” that contains main the elements’ “priori knowledge” – the set of basic laws/links/constants that make the system to be as it is.

I.e. in everything, including, say in an atom, a stone, etc. in Matter, every element – electrons and nucleus in an atom, atoms in a stone, etc., have absolutely obligatorily corresponding priori knowledge about what are “electron” and nucleus in atom, in stone atoms about what are other atoms, etc., and what are the laws/links constants in accordance with they compose atom, stone, etc.

At that everything in Matter has complete priory knowledge about everything in Matter, so always completely correctly logically analyze concrete current information about external and behave in accordance with this information; but know [practically] nothing else. So the everything don’t interact with anything behind material structures., i.e. Matter is some automaton, which so is rather stable in the Set.

Any consciousness fundamentally differs from any material structure just in that she is able, in principle, obtain arbitrary information in the Set, and, though she is organized basing of corresponding own concrete set of laws/links/constants, analyze the information by using logical rules, etc., forming so some “conscious” [non-automatic] “knowledge”.

The last really isn’t some “instinctive” property of consciousness, that is, again, is “automatic” consequence of that Logical Rules are “Logos” elements, but that is concretely “written” in concrete consciousnesses “program shells” structures.

The post is rather long already, so last note: the thread question really is rather vague. There can be innumerous “priori knowledge” in innumerous concrete cases – in every case to analyze any new information about something completely obligatorily it is necessary to have some priori knowledge about this something,

- including priori knowledge “I haven’t priory knowledge”, what results really in formulating priori knowledge as some priory assumptions, etc.. Without this there cannot be any knowledge, besides “instinctive”, which is two types - “automatic” above, and “concretely instinctive”, the last say, for humans are how to eat, to breath, to be reproduced, etc.

More see the link above.

Cheers

That 1+1 equals 2 is arguably a priori, but not instinctual.

1)

https://www.researchgate.net/publication/380396967_People_may_not_be_exactly_rational_but_upon_recognizing_their_disincentives_enough_they_can_only_act_so_irrational_What_do_you_think

2)https://www.researchgate.net/publication/380602676_Heuristic_vs_Random

About what is “priori knowledge” see the SS post above, including that in any case when someone considers some at least partially new, problem, he principally obligatorily always bases on some “priori knowledge”,

- so really in this case rather rarely some specific questions appear, as that this specific thread question is – what priori knowledge is instinctive for humans – and, as that is rigorously shown in the SS&VT explanation of what is the specific informational system “Consciousness”, that is true for all living beings on Earth.

Correspondingly that

“…That 1+1 equals 2 is arguably a priori, but not instinctual.…..”

- looks as rather vague claim. For any human that “1+1 equals 2” means nothing till he leaned arithmetics, while this, and mathematics as a whole, is for concrete humans some priori knowledge that becomes a posteory one after he has learned math. Though, again, at the learning he always uses some priory knowledges, of course.

Again, see SS post above and links in the post, really instinctive knowledge for humans is of two types – “fundamentally instinctive”, first of all – for humans that don’t know the SS&VT “The Information as Absolute” conception, link to the paper see SS post above;

- and so “utmost fundamentally” instinctively use information, including, say, Logical Rules, having at that really no any imagination about what information is, why it is as it is, and for/by what mystic reasons/ways they have ability to use information, while that for/by mystic reasons/ways is often adequate to the reality, when they, again for/by mystic reasons/ways, obtain from something that aren’t other humans [and from other humans also, though], etc.

On next level of fundamentality humans interacts by using information with concrete other fundamental phenomena/notions [examples see in SS post above], i.e., say, move in space having no any rational non-instinctive knowledge about what is space, etc.

Though note, that after a human has read, and understood, the conception, this both levels fundamental knowledge becomes for him quite non-instinctive.

On the non-fundamental levels humans again uses concrete instinctive knowledge, say, that is necessary to breath and how to breath, etc., etc.

Etc., more see the SS posts and links in the posts

Cheers

In general, instincts may contribute to some forms of tribal knowledge, such as basic survival instincts, but not all tribal knowledge can be reduced to instincts. The distinction lies in the source and nature of knowledge: instincts are innate biological tendencies, while prior knowledge is independent of sensory experience and can be known through reason alone.